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 Physics, Astrophysics and Cosmology MPhys Hons (F3F5)
Physics, Astrophysics and Cosmology MPhys Hons  2019 Entry
UCAS Code
F3F5
Entry Year
2019
also available in 2018
A Level Requirements
AAA
see all requirements
see all requirements
Duration
Full time 4 Year(s)
Course Overview
Our MPhys Physics, Astrophysics and Cosmology degree develops your understanding of the relationship between the physical laws of the universe and the astrophysical and cosmological domains. The specialist teaching is informed by our worldleading activities in space and planetary science, observational astrophysics and particle cosmology, and culminates in an individual investigative research project and advanced options in year four.
You will obtain a thorough grounding in core physics areas such as Quantum Physics and Electromagnetism in your first year, Quantum Mechanics and Relativity in your second year, and Particle and Atomic Physics in your third year. Furthermore, this scheme also includes lectures on Astronomy, Astrophysics and Cosmology in your second year and Stellar Astrophysics and Big Bang Cosmology in your third year, as well as specialised laboratory work in Astrophysics and Cosmology.
In your third year, you also carry out an investigative Cosmology group project where you tackle a problem of current research.
In your final year, you will complete an extended research project on topics such as binary variable stars, cosmic radio noise, gravitational waves and cosmic inflation, and study subjects such as Cosmology and Advanced Relativity and Gravity. For your project work, you can use our onsite astronomical observatory which contains a 356mm SchmidtCassegrain reflecting telescope and other equipment for optical and radio astronomy.
Entry Requirements
Grade Requirements
A Level AAA
Required Subjects A level Mathematics grade A and A level Physics grade A
IELTS 6.0 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
Interviews Applicants may be interviewed before being made an offer.
Other Qualifications
International Baccalaureate 36 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL and Physics HL
BTEC May be considered alongside A level Mathematics and A level Physics.
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via ugadmissions@lancaster.ac.uk
Course Structure
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
Year 1

Basic Physics Skills / Communication Skills
This module is made up of both lectures and practical sessions, aiming to developing your communication skills through the preparation and delivery of a verbal presentation and written scientific report.
The lectures will allow you to consider systematic approaches to problem solving including good methods in working and presenting answers, and in selecting and testing maths expressions in modelling.
You’ll also develop a theoretical understanding of the basic principles of measurement and recordkeeping, and will look at the best methods for assessing the significance of experimental data through consideration of uncertainties and statistical analysis.
Your practical sessions develop your skills and awareness for implementing informed career decisions. You’ll also explore the need for ethical behaviour, both in the context of an undergraduate physics degree and scientific research in general.

Classical Mechanics
In Classical Mechanics students will apply the ideas of fundamental Newtonian mechanics to real largescale systems such as rotating bodies, planetary systems and classical fluids.
The focus is on gravitation and its central importance in determining the largescale behaviour of the Universe. Concepts such as inertial and gravitational mass, Mach's principle, black holes and even dark matter will be explored.
This module will consider how to extend the principles of basic kinematics and dynamics to rotational situations, giving students an understanding of concepts of torque, moment of inertia, centre of mass, angular momentum and equilibrium.
Time will be spent looking at how to describe basic processes in the properties of materials including elasticity of solids and fluid dynamics.

Complex methods
This module provides an introduction to the concept of complex numbers and how they relate to applications in modelling physical ideas.
You’ll begin by investigating the principle of complex representation, looking at real and imaginary numbers, complex conjugation, Argand diagrams and different representations of complex numbers, such as Cartesian, polar, and exponential.
You’ll then develop skills in the manipulation of complex functions and the determination of the complex roots of equations. You’ll also consider physical applications, such as the use of complex methods in AC circuit analysis, the complex representation of harmonic waves, and the solution of differential equations describing damped oscillatory motion.

Electric and Magnetic Fields
Covering the basic laws of electromagnetism, this module allows students to investigate the similarities and differences between electric and magnetic fields, and to explore the basic concepts of electromagnetic phenomena including charge, current, field, force and potential.
The module will begin by studying electrostatics, describing forces and fields due to charge distributions using Coulomb's law and Gauss's law. Students will also look at the concept of polarisation, and how this can be applied to capacitance and combinations of capacitors.
Later on, the module will introduce magnetostatics, and students will learn how to describe it using the concepts of field, flux and force, and the motion of charged particles in a magnetic field. They will also look at the origins of magnetic fields and Ampere's law, and Faraday's law of electromagnetic induction.

Electrical Circuits & Instruments / Practical Lab II
This exciting module has practical emphasis. Through exploration of the effect of simple electrical components in DC and AC circuits you’ll build an understanding of the basic principles determining the behaviour of voltage and current in DC and AC circuits, and you’ll learn to quantitatively analyse circuits containing resistance, capacitance and inductance.
Working in the laboratory, you’ll gain practical experience of using instruments and experimental equipment, and develop your skills in making experimental measurements, recording and analysing data, and report writing.

Functions and differentiation
Mathematical functions are used to describe physical phenomena and their graphical representation.
This module is ideal for students wanting to gain a sound understanding of algebra, vectors and differentiation, and provides the tools needed for solving elementary equations involved in mathematical modelling, while strengthening problemsolving skills.
During the course, you’ll consider the fundamental principle of differentiation, and its relation to the slope of a graph. You’ll also learn how to differentiate basic functions directly, and how to use systematic techniques for combinations of functions.

Integration
This module is ideal for students looking for a firm grounding in integration techniques.
The module opens with an exploration of the fundamental principle of singlevariable integration and its relation to the area under a graph. This allows us to directly integrate a variety of basic functions of one variable.
You’ll then consider systematic techniques to tackle more complicated integrals of one variable including integration by parts and by substitution.
Finally you’ll study the important basic integrals over lines, areas and volumes.

Optics & Optical Instruments / Practical Lab III
In this module you’ll be introduced to the principles of geometrical optics and will learn how to practically apply them to instruments and experimental equipment in a laboratory setting, giving you a practical reference for the physical principles discussed in your lectures.
You’ll develop your understanding of commonly encountered optical phenomena, use geometrical optics to analyse optical systems, and understand the functions and basic principles of operation of some important optical instruments.

Oscillations & Waves / Practical Lab I
This exciting practical module on Oscillations and Waves allows you to investigate how wave and oscillatory phenomena arising in quite different areas of physics can be described in a very similar way, focusing in particular on the widely applicable model of simple harmonic motion.
You’ll then learn to recognise the wave equation and will develop the ability to solve it for a general situation, to calculate appropriate physical parameters describing a wave, and understand universal wave phenomena such as interference, beats and wave packets.
Part of this module is taught in the laboratory, giving you the opportunity to work with a wide range of measurement instrumentation. Through your practical work you’ll also gain an appreciation for the importance of uncertainties in experimental measurements and how to apply them in an appropriate manner.

Quantum Physics
The ultimate description of the Universe requires quantum and not classical mechanics. This module begin by investigating how specific experiments led to the breakdown of classical physics, before moving into the quantum world.
Students will look at the basic ideas of wave mechanics, particularly wave particle duality, as well as considering the probabilistic nature of phenomena and the uncertainty principle through the Schrodinger equation and its solution for simple situations.
Other topics that will be studied include the photoelectric effect, the nuclear atom and single slit diffraction. Ultimately, the students will be able to apply their knowledge to modelling real phenomena and situations.

Series and Differential Equations
This module develops knowledge of series and functions as well as introducing ordinary differential equations and methods of solving them.
You’ll first gain a good grounding in series and their formal representation, including geometric series, binomial expansion and the Taylor expansion. You’ll then learn to describe the representation of functions by series, using trigonometric and exponential functions.
In the second part of the module you’ll explore differential equations and their role in physics, including separable first order differential equations, second order differential equations for conservative systems and the method of integrating multiplier. As part of this you’ll also look at physical examples such as driven systems, harmonic force and the phenomenon of resonance.

The Physical Universe
In this module students will have the opportunity to explore the nature and methods of physics by considering the different scales of the Universe and the areas of physics which relate to them.
They will model real phenomena and situations, looking at the physical principles which are fundamental to mechanics, particularly Newton’s laws relating to forces and motion, and the principles of the conservation of energy and momentum.
Later on, the Special Theory of Relativity will be the main focus, beginning with Einstein's postulates and moving on to inertial reference frames, the physics of simultaneity, length contraction and time dilation, and spacetime diagrams.

Thermal Properties of Matter
This module focuses on the study of the thermal properties of matter, during which the students will gain an understanding of how to relate them to the fundamental mechanical properties of systems.
It will begin with an introduction to the concepts of temperature and heat, thermal equilibrium and temperature scales. Then students will look at how to describe mechanisms of heat transfer, particularly in phase changes and equations of state, and the kinetic model of an ideal gas.
As part of the module students will also have the opportunity to explore the first and second laws of thermodynamics, including concepts of internal energy, heat and work done, heat engines and refrigerators, and entropy. They will then learn about the role of thermodynamics in describing macroscopic physical situations, looking in particular at temperature, entropy, work, heat, and internal energy.

Vector Calculus
This module is ideal for students looking to develop their understanding of vector algebra and coordinate geometry in a physical context, extending elementary ideas of functions and calculus to a threedimensional description based on vector fields and potentials.
You’ll begin by exploring the real functions of many variables and their partial derivatives, followed by implicit differentiation of the functions of many variables and the chain rule. You’ll then go on to study the gradient vector in three dimensions in relation to directional derivatives, and will investigate the divergence and curl of a vector field as well as Stokes' theorem and the divergence theorem.
Vector Calculus places a focus on calculus in higher dimensional space, allowing you to develop your knowledge of parametric representations of curves, surfaces and volumes, calculation of areas and volumes including the use of changes of variables and Jacobians, and the calculation of line and surface integrals.

Vectors & Vector Algebra / IT Skills
This module will introduce you to the methodology of vectors and vector algebra, including their application to threedimensional motion, during a series of lectures and practical sessions.
You’ll learn to recognise the orthogonality of the dimensions of space and use vectors to describe them; demonstrate a facility with the techniques of vector algebra, including the use of vector products; and be able to apply this knowledge to modelling real phenomena and situations.
The practical element of the course sees you working in one of our PC labs learning how to best utilise spreadsheets and symbolic computations, and how to present data.
Core
Year 2

Astronomy
This module provides students with a modern perspective on the Universe, including its size and structure. Students will investigate electromagnetic radiation and will gain an understanding of telescopes and their limitations. The module will also present basic ideas of orbits, Kepler's Laws and common astronomical phenomena in the Solar System which are orbit related.
Additionally, students will make various observations on the structure of the Sun, and will develop their knowledge of distant objects, including different types of galaxies, interacting galaxies, active galaxies and exotic objects, whilst contrasting historical models of the Universe.

Astrophysics I
Students will receive an overview of directly measurable physical characteristics of stars, such as luminosity, spectroscopy, stellar atmospheres and composition. The module covers the HertzsprungRussell diagram and physics of Stellar Stability, and students will learn about energy generation in stars, energy transport in stellar interiors, and star birth.
Students will develop the ability to demonstrate how classical physics is successful in modelling many properties of main sequence stars and in explaining their formation and evolution. Additionally, more complex stellar behaviour that cannot be understood on the basis of classical physics will be introduced. Students will gain the skillset required to perform calculations relating to gravitational collapse, stability, lifetime and energy generation in wellbehaved main sequence stars and in nebulae.

Cosmology I
The module covers the structure of the Universe from the modern perspective, examining its size and structure, galaxies and galaxy clusters, dark matter and cosmic length and mass scales. Students will learn methods of measuring astronomical and cosmological distances and Hubble’s Law of Expansion.
Students will additionally encounter topics such as cosmic microwave radiation and physical phenomena in the very early universe, known as the Big Bang, through a mixture of lectures and seminars. Finally, the module will discuss the Universe’s ultimate fate.

Electromagnetism, Waves and Optics
This module provides students with a working knowledge of electromagnetion through Maxwell’s equations using the tools of vector calculus. Students will become familiar with the common connections between the many different phenomena in nature that share the mathematical model of a harmonic oscillator or of a wave. This module addresses the basic properties of wave propagation, diffraction and inference, and laser operation.
Students will develop an appreciation for the power of vector calculus and Maxwell’s equations for the description of electromagnetic phenomena, and will gain practical knowledge of Fresnel and Fraunhofer diffraction, as well as thinfilm interference fringes and antireflection coatings. Additionally, the module aims to enhance students’ understanding of the origin of polarisation, and the relevance of dichroism, along with an understanding of the basic elements of a laser, laser operation and important features of laser light.

Maths I
Designed to provide students with a working knowledge of the basic mathematical techniques that are required when studying physics at degree level and beyond, this module’s range of topics include a look at linear algebra, where students will discover coupled linear equations, linear transformations and normal modes of coupled oscillators. A section on Hilbert space will address wave equation, bases of functions and Kronekker deltasymbol, and angular harmonics will be covered in detail.
Over the duration of the module, students will become familiar with Pauli matrices, eigenvalues, eigenvectors and commutation relations, and will develop a range of skills and techniques required for solving various common types of linear equations. Additionally, a workshop led by postgraduate teaching assistants will be held every two weeks to provide extra onetoone tuition and support with coursework assignments as required.

Maths II
This module introduces the Fourier series and transforms, and addresses their application to examples in physics. Students will learn how to express a periodic function as a Fourier series, and find the Fourier transform of a function.
Additionally, students will solve linear ODEs and PDEs using Fourier techniques, as well as developing the ability to solve problems with initial conditions and/or spatial boundary conditions.

Quantum Mechanics
Students will be introduced to various axioms for quantum mechanics, such as eigenvalues, diagonalisation, differential and matrix operators and commutation relations. They will also learn about rotations and angular momentum, the interaction of magnetic moment with static magnetic field and electron spin. Students can expect to investigate approximation methods, such as the timedependent RayleighSchrodinger perturbation theory, and time dependent interactions, including the Heisenberg picture and time dependent Hamiltonians.
Students will learn to apply quantum mechanics to problems in one and three dimensions, including the hydrogen atom, by solving the Schrödinger equation, and will develop the ability to find approximate solutions for not exactly solvable systems. The module will enhance students’ understanding of expectation values and probabilities in the context of experiments on quantum systems, along with an appreciation for the mathematical consistency of quantum mechanics.

Relativity, Nuclei and Particles
Students receive an introductory conceptsbased approach to the module, giving a basic understanding of nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass and binding energy. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles.
By the end of the module, students will gain a working knowledge of Einstein’s theory of special relativity, both conceptually and mathematically, and will understand why the theory has replaced Newton’s concepts of absolute space and time. Additionally, students will develop a broad understanding of the equivalence principle and its relevance for general relativity.

Scientific Programming and Modelling Project
Introducing programming basics, this module engages students with the writing and compiling of computer programs in JAVA that can be used for numerical simulation and data analysis. This will involve variable types, input and output, and mathematical functions. Students will become familiar with debugging: the identification and classification of programming errors, and will explore method arguments and signatures, in addition to gaining knowledge of one dimensional, multidimensional and passing arrays.
Students will gain the necessary knowledge to model simple physical systems using appropriate programming techniques, and will develop an understanding of numerical precision and accuracy. By learning Object Orientated programming, students will use objects and methods to represent physical systems, class design, class testing and documentation in order to independently complete an openended project to model a physicsbased problem.

Thermal Properties of Matter
This module provides a review of thermodynamic equilibrium, temperature, zeroth law, reversible and irreversible processes, as well as heat, work and internal energy. Students will be introduced to the Boltzmann distribution and apply the Boltzmann distribution to solids, paramagnetism, heat capacity, defects in solids. The module offers students the opportunity to explore crystal structure and symmetry, lattices, symmetry operations and unit cells. Students will investigate the quantum mechanical free electron model and basic band structure ideas in nearly free electron and tight binding pictures as part of the module.
Students will develop an appreciation for the connections between the microscopic and macroscopic pictures of the thermal properties of solids, and will gain the skillset required to account for some fundamental properties of solids in statistical terms. Additionally, students will become familiar with the use of thermodynamic potentials and associated thermodynamic relations, and will gain an awareness of the different kinds of phase transition and how they are classified. Finally, students will gain the necessary knowledge required to understand the evidence for the third law of thermodynamics and how it relates to the unattainability of absolute zero.
Core
Year 3

Astrophysics II
Providing an expansion to topics covered in Astrophysics I, this module teaches students about stellar structure and stability, before moving on to thermonuclear fusion and stellar collapse. Students will discover degenerate objects, such as white dwarves and neutron stars, and will investigate xray and high energy astrophysics.
By the end of the module, students will understand the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to current understanding of stars and astrophysical phenomena. Students will also be able to describe recent astrophysical discoveries and review phenomena observed through the latest technological advances. Ultimately, students will gain knowledge in the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to our understanding of stars and astrophysical phenomena, and will gain an awareness recent astrophysical discoveries and review phenomena observed through the latest technological advances.

Astrophysics Laboratory
This module will familiarise students with astronomical experimentation and instrumentation. This includes practical use of a telescope, CCD cameras as well as manipulation of images taken with such instrumentation. Computer simulations will develop students’ understanding of key concepts in observational astronomy and students are encouraged to devise and perform any additional measurement or modelling which they think might give further insights into the physics investigated.
The laboratory is structured around a series of experiments which are intended to each last one working day. Students take a selection of these throughout the five weeks of the module. At the end of the module, students are required to write a more indepth report on just one of the weekly activities, supported not only by the results they obtained but also demonstrate additional reading into the physics and astronomy to which the work relates.
On completion, students will be able to make simple measurements using the telescope, spectroscope and CCD camera, in addition to developing an understanding of basic astronomical phenomena through computer simulations. Students will gain an appreciation for the statistical nature of astrophysical knowledge through analysis of stellar data relating to luminosity and temperature, and will be acquainted with some of the problems involved in satellitebased activities.

Atomic Physics
This module introduces oneelectron atoms and the spinorbit magnetic interaction, along with identical particles and the Helium atom. Students will investigate the Fermi gas model and the single particle shell model, and will compare predictions of the shell model for nuclear spins, parities and magnetic moments with experimental results. The module explores the nuclear beta decay process and the Fermi and Gamow  Teller selection rules, and students are provided with a description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.
Students will develop their knowledge in atomic and nuclear physics to an advanced level, and will be able to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure, in addition to gaining the ability to describe the processes of atomic transitions and nuclear decays. The module will provide an explanation of the concept and importance of the parity of an atomic or nuclear state, and will provide students with the opportunity to study the nuclear beta decay process and in particular the neutrino and parity nonconservation.

Cosmology Group Project
Students will work as part of a team and will receive guidance on project management, planning and meetings. Students will prepare a group report and will also give an individual talk at the third year miniconference, in addition to developing a research project with formulation, literature searches, data gathering, analysis and presentation.
The module provides an understanding of modern cosmology, including the areas where our understanding is still incomplete. In addition, students will investigate an openended Cosmologybased problem and will gain awareness of the tasks associated with a research project in Cosmology.

Cosmology II
The module explores the global dynamics of the Universe, the Friedmann equation, energy conservation and acceleration equations. The constituents of the Universe content and their evolution with time are then investigated. Students will examine the early Universe and the radiation era of the Hot Big Bang. The thermal history of the Hot Big Bang cosmology and Cosmic Inflation is studied as part of the module, along with the formation of largescale structure (galactic clusters and superclusters) in the Universe.
Students will develop awareness of our current understanding of the observed Universe and the early Universe, and will be able to write down some of the equations that encode this understanding. Students will also follow new developments at the level of journals like Nature and Scientific American.

General Physics Examination Paper
Students will be examined on material in core physics modules from year one, two and three. There will be a series of workshops in the Lent term, prior to the final examination, for discussion about the types of question set on the examination paper and the revision of problem solving and modelling techniques.
The module examines basic physics principles by applying them in situations that span the specific modules used to teach the course. This module will allow students to demonstrate a broad grasp of physics principles. Ultimately, students will be well practised in the application of physics methodology to a wide range of specific problems.

Particle Physics
The module explores symmetries, the Quark model and gives an introduction to QCD. Students will explore leptons, as well as forces and their carrier particles and Feynman diagrams. The module aims to provide a general introduction to theoretical and experimental topics in elementary particle physics, essentially the Standard Model of particle physics.
Students will gain the ability to describe the main features of the Standard Model of particle physics and understand its place in physics as a whole, and will be able to identify major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used, such as accelerators and detectors. In addition, students will understand the role of symmetry and conservation laws in fundamental physics, and will develop the ability to perform calculations of physically observable quantities relevant to the subject, along with solving problems based on the application of the general principles of particle physics.

Solid State Physics
The module offers an introduction to reciprocal lattice and diffraction of waves, the electronic band structure in metals, and insulators and semiconductors. Students will explore electrons in semiconductors, effective mass and the heat capacity of solids. There will be a Summary of experimental phenomena, tunnelling, Josephson Junctions and an outline of BCS theory.
Students will be introduced to theoretical and experimental topics in solid state physics at an advanced level, and will develop an understanding of the main features of the physics of electrons in solids, along with knowledge of the main features of the optical properties of solids.
Students will gain an enhanced understanding of crystal lattices and phonons, along with the main features of the thermal properties of solids, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.

Statistical Physics
This module explores the ideas, techniques and results of statistical physics. Students will examine gases and the density of states, along with the statistics of gases, fermions and bosons and the two distributions for gases. MaxwellBoltzmann gases, velocity distribution and fermiDirac gases are investigated as the module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics.
Students will provide a unified survey of the statistical physics of gases, including a full treatment of quantum statistics, gaining a fuller insight into the meaning of entropy. Students will gain knowledge in applications of statistics to various types of gas. Ultimately, students will develop the ability to apply expressions and distributions in order to form accurate deductions, for example using the Boltzmann distribution for the probability of finding a system in a particular quantum state. Additionally, students will learn the role of statistical concepts in understanding macroscopic systems, and will be able to describe superfluidity in liquid helium, BoseEinstein condensation and black body radiation.
Core

Computer Modelling
Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Java, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.
Students will develop a more thorough knowledge of the java language, including the use of inheritance, and will be able to write a physics modelling program in java.

Energy
The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative smallscale energy sources.
By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

Flavour Physics
The module will cover various topics including CKM matrix and its parameterisations; unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current topics of heavy flavour physics, such as c and bhadron production and decay analysis, along with top quark physics.
Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector, neutrino oscillations and will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

Groups and Symmetries
The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles.
By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

Lasers and Applications
This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing.
By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers. Students will understand the many uses of lasers in industry, medicine and the environment.

Matter at low temperature
The module begins by discussing what physicists mean by high and low temperatures, and looks at the different types of ordering that may occur as systems cool. Students will explore cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Students will observe the new phenomena that occur when systems are cooled below room temperature and will consider electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. The module provides an overview of the practical uses in superconducting quantum interference devices (SQUIDs).
The module seeks to explore a selection of fascinating phenomena that occurs when cooling matter to temperatures more than a million times colder than the familiar 290K of everyday life and observe the significance for both physics and technology. Additionally, students will appreciate the relation between temperature and order, will know how low temperatures are produced, including dilution refrigerators, and will also be able to describe the phenomena of superconductivity and superfluidity.

Physics of Fluids
Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.
Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the twofluid model of plasmas.
Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of NavierStokes equations, along with the wider applications of the NavierStokes theory to bio, geo and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

Physics of Living Systems
This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an informationprocessing system and the interactions between cardiovascular oscillations and brain waves.
Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.
Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then apply their knowledge of physics and mathematics to the understanding of basic principles of living systems – starting from a cell to the cardiovascular system and the brain.

Quantum information processing
The module consolidates the theoretical concepts of quantum information processing, exploring Dirac notation, density matrices and evolution, and entanglement. Students will also explore qubits, quantum algorithms, circuit design and error connection. In addition, the module will address trapped ions and atoms, Josephson junctions and quantum optics.
By the end of the module, students will be familiar with the fundamental concepts of quantum processing, such as density matrices and the dynamics of quantum systems, and will be able to understand how these can be implemented in realistic devices. Students will learn about experimental implementation based on atomoptical realisations and realisations in the solid state, and will apply these to explore theoretical concepts that have a vast area of application in condensed matter physics and atomquantumoptics.

Space and auroral physics
Information for this module is currently unavailable.
Optional
Year 4

Advanced Relativity and Gravity
The module offers a short review of special relativity, tensor calculus on Minkowski spacetime, differential calculus on Minkowski spacetime, and curved spacetimes. Students will explore general relativity, gravity as intrinsic curvature of spacetime, and the Einstein equations, along with predictions of the linearized Einstein equations, gravitational waves, and gravitomagnetic field equations. Students will investigate exact solutions of the Einstein equations, black holes and event horizons.
By the end of the module, students will have a basis knowledge and understanding of the theories of special and general relativity, and possess a conceptual understanding of the links between Newtonian mechanics and relativity. The module also provides a geometrical insight into the properties of spacetime and relativity.

Astrophysics III : Galaxies
Information for this module is currently unavailable.

Cosmology III
This module introduces students to the concepts of modern inflationary cosmology, and offers a review of BigBang cosmology. Topics featured on this module include cosmological equations, the concept of pressure in cosmology and the thermal universe.
Students will develop a greater understanding of the observed universe and will study evidence for recent acceleration of the expansion rate from luminosity distance versus redshift plots. Additionally, students will gain an enhanced knowledge of the angular power spectrum of the cosmic microwave background radiation.

MPhys Literature Review
Information for this module is currently unavailable.

MPhys Project
MPhys projects vary from year to year and are tailored to suit the individual student and the available research facilities. This twomodule project commences with a dissertation or literature review. Students will write a report on the project work and will conduct a presentation for the miniconference in the summer term, along with gaining skills related to oral presentation of scientific research.
Project work gives students the opportunity to carry out research or a detailed investigation into a specific area of physics appropriate to their chosen degree theme. Students will develop and apply analytical and problemsolving skills in an open ended situation, involving use of the library, computer, and other resources as appropriate, working alone or in a small group.
By the end of this module, students will demonstrate the ability to plan, manage and execute an investigation an area of physics in a systematic way using appropriate techniques. They will formulate conclusions and critically compare with relevant theory, and may be required to generate and analyse data and critically assess experimental uncertainties.
Core

Advanced Electrodynamics and Gravity
This module introduces a range of geometry and exterior calculus, including scalar fields, vector fields and convector fields. Students will explore pforms, exterior derivative, metrics and Hodge dual, and will discover electrodynamics, more specifically Maxwell equations in terms of the Maxwell 2form, 4velocity fields and Lorentz force equation in terms of the Maxwell 2form. Gravity is also covered, and students will engage in topics such as Einstein 3forms, stressenergymomentum 3forms and Einstein equations. Additionally, students will gain knowledge of killing vectors, spacetimes with symmetry, conserved quantities and black holes.
Students will gain the knowledge required to display an understanding of the intrinsic, covariant nature of electrodynamic, along with a familiarity with handling the Einstein equations and field equations on curved spacetime. Students will also be able to formulate and tackle field theories on spacetime using tools from modern differential geometry.

Advanced Magnetism
Students will be offered a revision of elements of the theory of electromagnetism, before being introduced to the phenomenology of solid state magnetic phenomena. The module discusses Van Vleck's description of diamagnetism and diamagnetism as quantum phenomenon. Students will explore ferromagnetism and antiferromagnetism, ferromagnetic exchange and the Heisenberg model, which includes selfconsistent mean field theory. A description of ferromagnetic phase transitions and Curie temperature will be provided as part of the module, along with the elements of the GinzburgLandau theory of magnetic phase transitions.
By the end of the module, students will develop a knowledge and understanding of magnetic and electric phenomena in condensed matter physics, in addition to an enhanced awareness of recent advances and current problems in condensed matter physics.

Computer Modelling
Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Java, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.
Students will develop a more thorough knowledge of the java language, including the use of inheritance, and will be able to write a physics modelling program in java.

Energy
The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative smallscale energy sources.
By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

Experimental Methods in Particle Physics
Students will study particle detection and experiments, exploring discoveries in particle physics and statistical tests, electroweak symmetry breaking and the Higgs mechanism. The module allows students to investigate CP violation and neutrino oscillations, and provides an introduction to supersymmetry and extensions to the standard model of particle physics.
By the end of the module, students will reinforce their knowledge and understanding of particle physics, and will gain a basic knowledge of experimental measurement and analysis techniques used in modern day particle physics research. Students will also develop an awareness of some recent advancements and current problems in particle physics research, and will go on to describe the successes and weaknesses of the standard model of particle physics and the possible theoretical extensions.

Flavour Physics
The module will cover various topics including CKM matrix and its parameterisations; unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current topics of heavy flavour physics, such as c and bhadron production and decay analysis, along with top quark physics.
Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector, neutrino oscillations and will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

Gauge Theories
The module covers various topics including Lagrangians and gauge transformations, global and local gauge invariance, gauge group and its representations and QED as a gauge theory. Students will explore QCD and nonabelian theories, asymptotic freedom and renormalisation group equation. The module discusses spontaneous symmetry breaking and Higgs mechanism, gauge structure of the electroweak theory, grand unified theories and extensions of the Standard Model.
By the end of the module, students will understand the modern phenomenology of the Standard Model of fundamental particles and will gain the mathematical background and physical insight into the fieldtheoretical structure of the Standards Model. Students will have an increased awareness of modern developments in Quantum Field Theory.

Groups and Symmetries
The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles.
By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

Lasers and Applications
This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing.
By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers. Students will understand the many uses of lasers in industry, medicine and the environment.

Matter at low temperature
The module begins by discussing what physicists mean by high and low temperatures, and looks at the different types of ordering that may occur as systems cool. Students will explore cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Students will observe the new phenomena that occur when systems are cooled below room temperature and will consider electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. The module provides an overview of the practical uses in superconducting quantum interference devices (SQUIDs).
The module seeks to explore a selection of fascinating phenomena that occurs when cooling matter to temperatures more than a million times colder than the familiar 290K of everyday life and observe the significance for both physics and technology. Additionally, students will appreciate the relation between temperature and order, will know how low temperatures are produced, including dilution refrigerators, and will also be able to describe the phenomena of superconductivity and superfluidity.

Physics of Fluids
Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.
Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the twofluid model of plasmas.
Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of NavierStokes equations, along with the wider applications of the NavierStokes theory to bio, geo and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

Physics of Living Systems
This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an informationprocessing system and the interactions between cardiovascular oscillations and brain waves.
Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.
Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then apply their knowledge of physics and mathematics to the understanding of basic principles of living systems – starting from a cell to the cardiovascular system and the brain.

Quantum transport in Low Dimensional Nanostructures
Students can expect to explore twodimensional electron systems, quantum transport in disordered lowdimensional electron systems and semiconductor quantum wires. The LandauerButtiker conductance formula is investigated, focusing on impurities in quantum wires, electronic transport in a magnetic field and the Hall effect. The module considers metallic point contacts, the pointcontact spectroscopy of the electronphonon interaction, and atomic breakjunctions and the scanning tunnelling microscope. Students will receive examples of applications of scanning tunnelling microscopy as part of the module.
By the end of the module, students will have knowledge of the physics of nanoscale solid state devices and how these may be manufactured and utilised. They will enhance their awareness of the recent advancements and current problems in condensed matter physics.

Semiconductor Device Physics
Students will familiarise themselves with crystal growth, including growth theory, faceting, impurity segregation and zone refining. The module presents students with a silicon case study, investigating semiconducting properties, silicon oxide, masking, surface pacification and photolithographic processing. Compound semiconductors will be discussed, covering band structure advantages over silicon, IIVI materials and effects of iconicity.
Additionally, students will explore thin film semiconductors, such as epitaxy, vapour phase growth, metalloorganic methods and liquid phase epitaxy, and the module provides a broad interdisciplinary overview of the linkage between the physics, chemistry and other materials sciences involved in the synthesis of semiconductors and the devices made from them.
By the end of the module, students will develop an understanding of the basic properties of crystals and crystal defects, and will be able to describe how crystals are grown and discuss the main semiconductor used for microelectronics as a detailed case study. Students will also demonstrate how physics continues to play a major role in enabling information technology.

SolarPlanetary Physics
Students will extend their knowledge on planetary systems, looking at the advances in planetary physics and planetary radiation environments. The module explores solarplanetary coupling and planetary magnetospheres, planetary magnetospheres within our solar system and unmagnetised bodies, such as Mars, the moon and comets. Students will study the heliosphere and beyond, investigating the sun’s influence on cosmic rays.
This module introduces students to the physical processes that dominate and characterise the planets in our solar system and those postulated to exist beyond. This will include the terrestrial planets, the outer planets and moons, the physics of planetary exploration, planetary astrophysics and the implications for life in the universe. Students will be required to carry out independent research on preset discussion topics and present their findings to the group in the form of oral presentations and posters in a series of seminars.
Students will be able to explain the key similarities and differences between the planets in the solar system, and will understand the role of a planet’s magnetic field in the retention of a gaseous atmosphere. Students will gain further skills such as the ability to calculate the scale size of a planet’s magnetosphere, and a developed knowledge of the important role of comparative planetology in our understanding of the solar system .In addition, students are required to undertake orbital mechanics calculations relevant to planetary systems and exploration.
Optional
Lancaster University offers a range of programmes, some of which follow a structured study programme, and others which offer the chance for you to devise a more flexible programme. We divide academic study into two sections  Part 1 (Year 1) and Part 2 (Year 2, 3 and sometimes 4). For most programmes Part 1 requires you to study 120 credits spread over at least three modules which, depending upon your programme, will be drawn from one, two or three different academic subjects. A higher degree of specialisation then develops in subsequent years. For more information about our teaching methods at Lancaster visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.
Careers
Careers
Physics is an exciting subject that is fundamental to the developments in modern society. Applications of the subject range from the very pure to the very practical, and a physics degree opens up a wide range of rewarding careers in scientific research and technological development, as well as in a variety of other professions. A substantial number of our graduates continue on to postgraduate education, or enter employment that directly relies on their specialist skills. Our students also find employment in careers where they are valued because of general skills gained during the course such as logical thinking, problem solving, numeracy and computer literacy. Examples include consulting, finance, computer programming, and accountancy, as well as managerial and administrative positions.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability/career development, campus community and social development. Visit our Employability section for full details.
Fees and Funding
Fees
We set our fees on an annual basis and the 2019/20 entry fees have not yet been set.
As a guide, our fees in 2018 were:
UK/EU  Overseas 

£9,250  £18,890 
Channel Islands and the Isle of Man
Some science and medicine courses have higher fees for students from the Channel Islands and the Isle of Man. You can find more details here: Island Students.
Funding
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
Students taking Part I of the course are charged £10 for a bound copy of the lab manual. There are a number of optional oneday visits to places of interest and students pay travel costs.
Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.

Course Overview
Course Overview
Our MPhys Physics, Astrophysics and Cosmology degree develops your understanding of the relationship between the physical laws of the universe and the astrophysical and cosmological domains. The specialist teaching is informed by our worldleading activities in space and planetary science, observational astrophysics and particle cosmology, and culminates in an individual investigative research project and advanced options in year four.
You will obtain a thorough grounding in core physics areas such as Quantum Physics and Electromagnetism in your first year, Quantum Mechanics and Relativity in your second year, and Particle and Atomic Physics in your third year. Furthermore, this scheme also includes lectures on Astronomy, Astrophysics and Cosmology in your second year and Stellar Astrophysics and Big Bang Cosmology in your third year, as well as specialised laboratory work in Astrophysics and Cosmology.
In your third year, you also carry out an investigative Cosmology group project where you tackle a problem of current research.
In your final year, you will complete an extended research project on topics such as binary variable stars, cosmic radio noise, gravitational waves and cosmic inflation, and study subjects such as Cosmology and Advanced Relativity and Gravity. For your project work, you can use our onsite astronomical observatory which contains a 356mm SchmidtCassegrain reflecting telescope and other equipment for optical and radio astronomy.

Entry Requirements
Entry Requirements
Grade Requirements
A Level AAA
Required Subjects A level Mathematics grade A and A level Physics grade A
IELTS 6.0 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
Interviews Applicants may be interviewed before being made an offer.
Other Qualifications
International Baccalaureate 36 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL and Physics HL
BTEC May be considered alongside A level Mathematics and A level Physics.
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via ugadmissions@lancaster.ac.uk

Course Structure
Course Structure
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
Year 1

Basic Physics Skills / Communication Skills
This module is made up of both lectures and practical sessions, aiming to developing your communication skills through the preparation and delivery of a verbal presentation and written scientific report.
The lectures will allow you to consider systematic approaches to problem solving including good methods in working and presenting answers, and in selecting and testing maths expressions in modelling.
You’ll also develop a theoretical understanding of the basic principles of measurement and recordkeeping, and will look at the best methods for assessing the significance of experimental data through consideration of uncertainties and statistical analysis.
Your practical sessions develop your skills and awareness for implementing informed career decisions. You’ll also explore the need for ethical behaviour, both in the context of an undergraduate physics degree and scientific research in general.

Classical Mechanics
In Classical Mechanics students will apply the ideas of fundamental Newtonian mechanics to real largescale systems such as rotating bodies, planetary systems and classical fluids.
The focus is on gravitation and its central importance in determining the largescale behaviour of the Universe. Concepts such as inertial and gravitational mass, Mach's principle, black holes and even dark matter will be explored.
This module will consider how to extend the principles of basic kinematics and dynamics to rotational situations, giving students an understanding of concepts of torque, moment of inertia, centre of mass, angular momentum and equilibrium.
Time will be spent looking at how to describe basic processes in the properties of materials including elasticity of solids and fluid dynamics.

Complex methods
This module provides an introduction to the concept of complex numbers and how they relate to applications in modelling physical ideas.
You’ll begin by investigating the principle of complex representation, looking at real and imaginary numbers, complex conjugation, Argand diagrams and different representations of complex numbers, such as Cartesian, polar, and exponential.
You’ll then develop skills in the manipulation of complex functions and the determination of the complex roots of equations. You’ll also consider physical applications, such as the use of complex methods in AC circuit analysis, the complex representation of harmonic waves, and the solution of differential equations describing damped oscillatory motion.

Electric and Magnetic Fields
Covering the basic laws of electromagnetism, this module allows students to investigate the similarities and differences between electric and magnetic fields, and to explore the basic concepts of electromagnetic phenomena including charge, current, field, force and potential.
The module will begin by studying electrostatics, describing forces and fields due to charge distributions using Coulomb's law and Gauss's law. Students will also look at the concept of polarisation, and how this can be applied to capacitance and combinations of capacitors.
Later on, the module will introduce magnetostatics, and students will learn how to describe it using the concepts of field, flux and force, and the motion of charged particles in a magnetic field. They will also look at the origins of magnetic fields and Ampere's law, and Faraday's law of electromagnetic induction.

Electrical Circuits & Instruments / Practical Lab II
This exciting module has practical emphasis. Through exploration of the effect of simple electrical components in DC and AC circuits you’ll build an understanding of the basic principles determining the behaviour of voltage and current in DC and AC circuits, and you’ll learn to quantitatively analyse circuits containing resistance, capacitance and inductance.
Working in the laboratory, you’ll gain practical experience of using instruments and experimental equipment, and develop your skills in making experimental measurements, recording and analysing data, and report writing.

Functions and differentiation
Mathematical functions are used to describe physical phenomena and their graphical representation.
This module is ideal for students wanting to gain a sound understanding of algebra, vectors and differentiation, and provides the tools needed for solving elementary equations involved in mathematical modelling, while strengthening problemsolving skills.
During the course, you’ll consider the fundamental principle of differentiation, and its relation to the slope of a graph. You’ll also learn how to differentiate basic functions directly, and how to use systematic techniques for combinations of functions.

Integration
This module is ideal for students looking for a firm grounding in integration techniques.
The module opens with an exploration of the fundamental principle of singlevariable integration and its relation to the area under a graph. This allows us to directly integrate a variety of basic functions of one variable.
You’ll then consider systematic techniques to tackle more complicated integrals of one variable including integration by parts and by substitution.
Finally you’ll study the important basic integrals over lines, areas and volumes.

Optics & Optical Instruments / Practical Lab III
In this module you’ll be introduced to the principles of geometrical optics and will learn how to practically apply them to instruments and experimental equipment in a laboratory setting, giving you a practical reference for the physical principles discussed in your lectures.
You’ll develop your understanding of commonly encountered optical phenomena, use geometrical optics to analyse optical systems, and understand the functions and basic principles of operation of some important optical instruments.

Oscillations & Waves / Practical Lab I
This exciting practical module on Oscillations and Waves allows you to investigate how wave and oscillatory phenomena arising in quite different areas of physics can be described in a very similar way, focusing in particular on the widely applicable model of simple harmonic motion.
You’ll then learn to recognise the wave equation and will develop the ability to solve it for a general situation, to calculate appropriate physical parameters describing a wave, and understand universal wave phenomena such as interference, beats and wave packets.
Part of this module is taught in the laboratory, giving you the opportunity to work with a wide range of measurement instrumentation. Through your practical work you’ll also gain an appreciation for the importance of uncertainties in experimental measurements and how to apply them in an appropriate manner.

Quantum Physics
The ultimate description of the Universe requires quantum and not classical mechanics. This module begin by investigating how specific experiments led to the breakdown of classical physics, before moving into the quantum world.
Students will look at the basic ideas of wave mechanics, particularly wave particle duality, as well as considering the probabilistic nature of phenomena and the uncertainty principle through the Schrodinger equation and its solution for simple situations.
Other topics that will be studied include the photoelectric effect, the nuclear atom and single slit diffraction. Ultimately, the students will be able to apply their knowledge to modelling real phenomena and situations.

Series and Differential Equations
This module develops knowledge of series and functions as well as introducing ordinary differential equations and methods of solving them.
You’ll first gain a good grounding in series and their formal representation, including geometric series, binomial expansion and the Taylor expansion. You’ll then learn to describe the representation of functions by series, using trigonometric and exponential functions.
In the second part of the module you’ll explore differential equations and their role in physics, including separable first order differential equations, second order differential equations for conservative systems and the method of integrating multiplier. As part of this you’ll also look at physical examples such as driven systems, harmonic force and the phenomenon of resonance.

The Physical Universe
In this module students will have the opportunity to explore the nature and methods of physics by considering the different scales of the Universe and the areas of physics which relate to them.
They will model real phenomena and situations, looking at the physical principles which are fundamental to mechanics, particularly Newton’s laws relating to forces and motion, and the principles of the conservation of energy and momentum.
Later on, the Special Theory of Relativity will be the main focus, beginning with Einstein's postulates and moving on to inertial reference frames, the physics of simultaneity, length contraction and time dilation, and spacetime diagrams.

Thermal Properties of Matter
This module focuses on the study of the thermal properties of matter, during which the students will gain an understanding of how to relate them to the fundamental mechanical properties of systems.
It will begin with an introduction to the concepts of temperature and heat, thermal equilibrium and temperature scales. Then students will look at how to describe mechanisms of heat transfer, particularly in phase changes and equations of state, and the kinetic model of an ideal gas.
As part of the module students will also have the opportunity to explore the first and second laws of thermodynamics, including concepts of internal energy, heat and work done, heat engines and refrigerators, and entropy. They will then learn about the role of thermodynamics in describing macroscopic physical situations, looking in particular at temperature, entropy, work, heat, and internal energy.

Vector Calculus
This module is ideal for students looking to develop their understanding of vector algebra and coordinate geometry in a physical context, extending elementary ideas of functions and calculus to a threedimensional description based on vector fields and potentials.
You’ll begin by exploring the real functions of many variables and their partial derivatives, followed by implicit differentiation of the functions of many variables and the chain rule. You’ll then go on to study the gradient vector in three dimensions in relation to directional derivatives, and will investigate the divergence and curl of a vector field as well as Stokes' theorem and the divergence theorem.
Vector Calculus places a focus on calculus in higher dimensional space, allowing you to develop your knowledge of parametric representations of curves, surfaces and volumes, calculation of areas and volumes including the use of changes of variables and Jacobians, and the calculation of line and surface integrals.

Vectors & Vector Algebra / IT Skills
This module will introduce you to the methodology of vectors and vector algebra, including their application to threedimensional motion, during a series of lectures and practical sessions.
You’ll learn to recognise the orthogonality of the dimensions of space and use vectors to describe them; demonstrate a facility with the techniques of vector algebra, including the use of vector products; and be able to apply this knowledge to modelling real phenomena and situations.
The practical element of the course sees you working in one of our PC labs learning how to best utilise spreadsheets and symbolic computations, and how to present data.
Core
Year 2

Astronomy
This module provides students with a modern perspective on the Universe, including its size and structure. Students will investigate electromagnetic radiation and will gain an understanding of telescopes and their limitations. The module will also present basic ideas of orbits, Kepler's Laws and common astronomical phenomena in the Solar System which are orbit related.
Additionally, students will make various observations on the structure of the Sun, and will develop their knowledge of distant objects, including different types of galaxies, interacting galaxies, active galaxies and exotic objects, whilst contrasting historical models of the Universe.

Astrophysics I
Students will receive an overview of directly measurable physical characteristics of stars, such as luminosity, spectroscopy, stellar atmospheres and composition. The module covers the HertzsprungRussell diagram and physics of Stellar Stability, and students will learn about energy generation in stars, energy transport in stellar interiors, and star birth.
Students will develop the ability to demonstrate how classical physics is successful in modelling many properties of main sequence stars and in explaining their formation and evolution. Additionally, more complex stellar behaviour that cannot be understood on the basis of classical physics will be introduced. Students will gain the skillset required to perform calculations relating to gravitational collapse, stability, lifetime and energy generation in wellbehaved main sequence stars and in nebulae.

Cosmology I
The module covers the structure of the Universe from the modern perspective, examining its size and structure, galaxies and galaxy clusters, dark matter and cosmic length and mass scales. Students will learn methods of measuring astronomical and cosmological distances and Hubble’s Law of Expansion.
Students will additionally encounter topics such as cosmic microwave radiation and physical phenomena in the very early universe, known as the Big Bang, through a mixture of lectures and seminars. Finally, the module will discuss the Universe’s ultimate fate.

Electromagnetism, Waves and Optics
This module provides students with a working knowledge of electromagnetion through Maxwell’s equations using the tools of vector calculus. Students will become familiar with the common connections between the many different phenomena in nature that share the mathematical model of a harmonic oscillator or of a wave. This module addresses the basic properties of wave propagation, diffraction and inference, and laser operation.
Students will develop an appreciation for the power of vector calculus and Maxwell’s equations for the description of electromagnetic phenomena, and will gain practical knowledge of Fresnel and Fraunhofer diffraction, as well as thinfilm interference fringes and antireflection coatings. Additionally, the module aims to enhance students’ understanding of the origin of polarisation, and the relevance of dichroism, along with an understanding of the basic elements of a laser, laser operation and important features of laser light.

Maths I
Designed to provide students with a working knowledge of the basic mathematical techniques that are required when studying physics at degree level and beyond, this module’s range of topics include a look at linear algebra, where students will discover coupled linear equations, linear transformations and normal modes of coupled oscillators. A section on Hilbert space will address wave equation, bases of functions and Kronekker deltasymbol, and angular harmonics will be covered in detail.
Over the duration of the module, students will become familiar with Pauli matrices, eigenvalues, eigenvectors and commutation relations, and will develop a range of skills and techniques required for solving various common types of linear equations. Additionally, a workshop led by postgraduate teaching assistants will be held every two weeks to provide extra onetoone tuition and support with coursework assignments as required.

Maths II
This module introduces the Fourier series and transforms, and addresses their application to examples in physics. Students will learn how to express a periodic function as a Fourier series, and find the Fourier transform of a function.
Additionally, students will solve linear ODEs and PDEs using Fourier techniques, as well as developing the ability to solve problems with initial conditions and/or spatial boundary conditions.

Quantum Mechanics
Students will be introduced to various axioms for quantum mechanics, such as eigenvalues, diagonalisation, differential and matrix operators and commutation relations. They will also learn about rotations and angular momentum, the interaction of magnetic moment with static magnetic field and electron spin. Students can expect to investigate approximation methods, such as the timedependent RayleighSchrodinger perturbation theory, and time dependent interactions, including the Heisenberg picture and time dependent Hamiltonians.
Students will learn to apply quantum mechanics to problems in one and three dimensions, including the hydrogen atom, by solving the Schrödinger equation, and will develop the ability to find approximate solutions for not exactly solvable systems. The module will enhance students’ understanding of expectation values and probabilities in the context of experiments on quantum systems, along with an appreciation for the mathematical consistency of quantum mechanics.

Relativity, Nuclei and Particles
Students receive an introductory conceptsbased approach to the module, giving a basic understanding of nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass and binding energy. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles.
By the end of the module, students will gain a working knowledge of Einstein’s theory of special relativity, both conceptually and mathematically, and will understand why the theory has replaced Newton’s concepts of absolute space and time. Additionally, students will develop a broad understanding of the equivalence principle and its relevance for general relativity.

Scientific Programming and Modelling Project
Introducing programming basics, this module engages students with the writing and compiling of computer programs in JAVA that can be used for numerical simulation and data analysis. This will involve variable types, input and output, and mathematical functions. Students will become familiar with debugging: the identification and classification of programming errors, and will explore method arguments and signatures, in addition to gaining knowledge of one dimensional, multidimensional and passing arrays.
Students will gain the necessary knowledge to model simple physical systems using appropriate programming techniques, and will develop an understanding of numerical precision and accuracy. By learning Object Orientated programming, students will use objects and methods to represent physical systems, class design, class testing and documentation in order to independently complete an openended project to model a physicsbased problem.

Thermal Properties of Matter
This module provides a review of thermodynamic equilibrium, temperature, zeroth law, reversible and irreversible processes, as well as heat, work and internal energy. Students will be introduced to the Boltzmann distribution and apply the Boltzmann distribution to solids, paramagnetism, heat capacity, defects in solids. The module offers students the opportunity to explore crystal structure and symmetry, lattices, symmetry operations and unit cells. Students will investigate the quantum mechanical free electron model and basic band structure ideas in nearly free electron and tight binding pictures as part of the module.
Students will develop an appreciation for the connections between the microscopic and macroscopic pictures of the thermal properties of solids, and will gain the skillset required to account for some fundamental properties of solids in statistical terms. Additionally, students will become familiar with the use of thermodynamic potentials and associated thermodynamic relations, and will gain an awareness of the different kinds of phase transition and how they are classified. Finally, students will gain the necessary knowledge required to understand the evidence for the third law of thermodynamics and how it relates to the unattainability of absolute zero.
Core
Year 3

Astrophysics II
Providing an expansion to topics covered in Astrophysics I, this module teaches students about stellar structure and stability, before moving on to thermonuclear fusion and stellar collapse. Students will discover degenerate objects, such as white dwarves and neutron stars, and will investigate xray and high energy astrophysics.
By the end of the module, students will understand the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to current understanding of stars and astrophysical phenomena. Students will also be able to describe recent astrophysical discoveries and review phenomena observed through the latest technological advances. Ultimately, students will gain knowledge in the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to our understanding of stars and astrophysical phenomena, and will gain an awareness recent astrophysical discoveries and review phenomena observed through the latest technological advances.

Astrophysics Laboratory
This module will familiarise students with astronomical experimentation and instrumentation. This includes practical use of a telescope, CCD cameras as well as manipulation of images taken with such instrumentation. Computer simulations will develop students’ understanding of key concepts in observational astronomy and students are encouraged to devise and perform any additional measurement or modelling which they think might give further insights into the physics investigated.
The laboratory is structured around a series of experiments which are intended to each last one working day. Students take a selection of these throughout the five weeks of the module. At the end of the module, students are required to write a more indepth report on just one of the weekly activities, supported not only by the results they obtained but also demonstrate additional reading into the physics and astronomy to which the work relates.
On completion, students will be able to make simple measurements using the telescope, spectroscope and CCD camera, in addition to developing an understanding of basic astronomical phenomena through computer simulations. Students will gain an appreciation for the statistical nature of astrophysical knowledge through analysis of stellar data relating to luminosity and temperature, and will be acquainted with some of the problems involved in satellitebased activities.

Atomic Physics
This module introduces oneelectron atoms and the spinorbit magnetic interaction, along with identical particles and the Helium atom. Students will investigate the Fermi gas model and the single particle shell model, and will compare predictions of the shell model for nuclear spins, parities and magnetic moments with experimental results. The module explores the nuclear beta decay process and the Fermi and Gamow  Teller selection rules, and students are provided with a description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.
Students will develop their knowledge in atomic and nuclear physics to an advanced level, and will be able to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure, in addition to gaining the ability to describe the processes of atomic transitions and nuclear decays. The module will provide an explanation of the concept and importance of the parity of an atomic or nuclear state, and will provide students with the opportunity to study the nuclear beta decay process and in particular the neutrino and parity nonconservation.

Cosmology Group Project
Students will work as part of a team and will receive guidance on project management, planning and meetings. Students will prepare a group report and will also give an individual talk at the third year miniconference, in addition to developing a research project with formulation, literature searches, data gathering, analysis and presentation.
The module provides an understanding of modern cosmology, including the areas where our understanding is still incomplete. In addition, students will investigate an openended Cosmologybased problem and will gain awareness of the tasks associated with a research project in Cosmology.

Cosmology II
The module explores the global dynamics of the Universe, the Friedmann equation, energy conservation and acceleration equations. The constituents of the Universe content and their evolution with time are then investigated. Students will examine the early Universe and the radiation era of the Hot Big Bang. The thermal history of the Hot Big Bang cosmology and Cosmic Inflation is studied as part of the module, along with the formation of largescale structure (galactic clusters and superclusters) in the Universe.
Students will develop awareness of our current understanding of the observed Universe and the early Universe, and will be able to write down some of the equations that encode this understanding. Students will also follow new developments at the level of journals like Nature and Scientific American.

General Physics Examination Paper
Students will be examined on material in core physics modules from year one, two and three. There will be a series of workshops in the Lent term, prior to the final examination, for discussion about the types of question set on the examination paper and the revision of problem solving and modelling techniques.
The module examines basic physics principles by applying them in situations that span the specific modules used to teach the course. This module will allow students to demonstrate a broad grasp of physics principles. Ultimately, students will be well practised in the application of physics methodology to a wide range of specific problems.

Particle Physics
The module explores symmetries, the Quark model and gives an introduction to QCD. Students will explore leptons, as well as forces and their carrier particles and Feynman diagrams. The module aims to provide a general introduction to theoretical and experimental topics in elementary particle physics, essentially the Standard Model of particle physics.
Students will gain the ability to describe the main features of the Standard Model of particle physics and understand its place in physics as a whole, and will be able to identify major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used, such as accelerators and detectors. In addition, students will understand the role of symmetry and conservation laws in fundamental physics, and will develop the ability to perform calculations of physically observable quantities relevant to the subject, along with solving problems based on the application of the general principles of particle physics.

Solid State Physics
The module offers an introduction to reciprocal lattice and diffraction of waves, the electronic band structure in metals, and insulators and semiconductors. Students will explore electrons in semiconductors, effective mass and the heat capacity of solids. There will be a Summary of experimental phenomena, tunnelling, Josephson Junctions and an outline of BCS theory.
Students will be introduced to theoretical and experimental topics in solid state physics at an advanced level, and will develop an understanding of the main features of the physics of electrons in solids, along with knowledge of the main features of the optical properties of solids.
Students will gain an enhanced understanding of crystal lattices and phonons, along with the main features of the thermal properties of solids, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.

Statistical Physics
This module explores the ideas, techniques and results of statistical physics. Students will examine gases and the density of states, along with the statistics of gases, fermions and bosons and the two distributions for gases. MaxwellBoltzmann gases, velocity distribution and fermiDirac gases are investigated as the module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics.
Students will provide a unified survey of the statistical physics of gases, including a full treatment of quantum statistics, gaining a fuller insight into the meaning of entropy. Students will gain knowledge in applications of statistics to various types of gas. Ultimately, students will develop the ability to apply expressions and distributions in order to form accurate deductions, for example using the Boltzmann distribution for the probability of finding a system in a particular quantum state. Additionally, students will learn the role of statistical concepts in understanding macroscopic systems, and will be able to describe superfluidity in liquid helium, BoseEinstein condensation and black body radiation.
Core

Computer Modelling
Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Java, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.
Students will develop a more thorough knowledge of the java language, including the use of inheritance, and will be able to write a physics modelling program in java.

Energy
The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative smallscale energy sources.
By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

Flavour Physics
The module will cover various topics including CKM matrix and its parameterisations; unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current topics of heavy flavour physics, such as c and bhadron production and decay analysis, along with top quark physics.
Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector, neutrino oscillations and will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

Groups and Symmetries
The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles.
By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

Lasers and Applications
This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing.
By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers. Students will understand the many uses of lasers in industry, medicine and the environment.

Matter at low temperature
The module begins by discussing what physicists mean by high and low temperatures, and looks at the different types of ordering that may occur as systems cool. Students will explore cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Students will observe the new phenomena that occur when systems are cooled below room temperature and will consider electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. The module provides an overview of the practical uses in superconducting quantum interference devices (SQUIDs).
The module seeks to explore a selection of fascinating phenomena that occurs when cooling matter to temperatures more than a million times colder than the familiar 290K of everyday life and observe the significance for both physics and technology. Additionally, students will appreciate the relation between temperature and order, will know how low temperatures are produced, including dilution refrigerators, and will also be able to describe the phenomena of superconductivity and superfluidity.

Physics of Fluids
Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.
Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the twofluid model of plasmas.
Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of NavierStokes equations, along with the wider applications of the NavierStokes theory to bio, geo and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

Physics of Living Systems
This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an informationprocessing system and the interactions between cardiovascular oscillations and brain waves.
Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.
Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then apply their knowledge of physics and mathematics to the understanding of basic principles of living systems – starting from a cell to the cardiovascular system and the brain.

Quantum information processing
The module consolidates the theoretical concepts of quantum information processing, exploring Dirac notation, density matrices and evolution, and entanglement. Students will also explore qubits, quantum algorithms, circuit design and error connection. In addition, the module will address trapped ions and atoms, Josephson junctions and quantum optics.
By the end of the module, students will be familiar with the fundamental concepts of quantum processing, such as density matrices and the dynamics of quantum systems, and will be able to understand how these can be implemented in realistic devices. Students will learn about experimental implementation based on atomoptical realisations and realisations in the solid state, and will apply these to explore theoretical concepts that have a vast area of application in condensed matter physics and atomquantumoptics.

Space and auroral physics
Information for this module is currently unavailable.
Optional
Year 4

Advanced Relativity and Gravity
The module offers a short review of special relativity, tensor calculus on Minkowski spacetime, differential calculus on Minkowski spacetime, and curved spacetimes. Students will explore general relativity, gravity as intrinsic curvature of spacetime, and the Einstein equations, along with predictions of the linearized Einstein equations, gravitational waves, and gravitomagnetic field equations. Students will investigate exact solutions of the Einstein equations, black holes and event horizons.
By the end of the module, students will have a basis knowledge and understanding of the theories of special and general relativity, and possess a conceptual understanding of the links between Newtonian mechanics and relativity. The module also provides a geometrical insight into the properties of spacetime and relativity.

Astrophysics III : Galaxies
Information for this module is currently unavailable.

Cosmology III
This module introduces students to the concepts of modern inflationary cosmology, and offers a review of BigBang cosmology. Topics featured on this module include cosmological equations, the concept of pressure in cosmology and the thermal universe.
Students will develop a greater understanding of the observed universe and will study evidence for recent acceleration of the expansion rate from luminosity distance versus redshift plots. Additionally, students will gain an enhanced knowledge of the angular power spectrum of the cosmic microwave background radiation.

MPhys Literature Review
Information for this module is currently unavailable.

MPhys Project
MPhys projects vary from year to year and are tailored to suit the individual student and the available research facilities. This twomodule project commences with a dissertation or literature review. Students will write a report on the project work and will conduct a presentation for the miniconference in the summer term, along with gaining skills related to oral presentation of scientific research.
Project work gives students the opportunity to carry out research or a detailed investigation into a specific area of physics appropriate to their chosen degree theme. Students will develop and apply analytical and problemsolving skills in an open ended situation, involving use of the library, computer, and other resources as appropriate, working alone or in a small group.
By the end of this module, students will demonstrate the ability to plan, manage and execute an investigation an area of physics in a systematic way using appropriate techniques. They will formulate conclusions and critically compare with relevant theory, and may be required to generate and analyse data and critically assess experimental uncertainties.
Core

Advanced Electrodynamics and Gravity
This module introduces a range of geometry and exterior calculus, including scalar fields, vector fields and convector fields. Students will explore pforms, exterior derivative, metrics and Hodge dual, and will discover electrodynamics, more specifically Maxwell equations in terms of the Maxwell 2form, 4velocity fields and Lorentz force equation in terms of the Maxwell 2form. Gravity is also covered, and students will engage in topics such as Einstein 3forms, stressenergymomentum 3forms and Einstein equations. Additionally, students will gain knowledge of killing vectors, spacetimes with symmetry, conserved quantities and black holes.
Students will gain the knowledge required to display an understanding of the intrinsic, covariant nature of electrodynamic, along with a familiarity with handling the Einstein equations and field equations on curved spacetime. Students will also be able to formulate and tackle field theories on spacetime using tools from modern differential geometry.

Advanced Magnetism
Students will be offered a revision of elements of the theory of electromagnetism, before being introduced to the phenomenology of solid state magnetic phenomena. The module discusses Van Vleck's description of diamagnetism and diamagnetism as quantum phenomenon. Students will explore ferromagnetism and antiferromagnetism, ferromagnetic exchange and the Heisenberg model, which includes selfconsistent mean field theory. A description of ferromagnetic phase transitions and Curie temperature will be provided as part of the module, along with the elements of the GinzburgLandau theory of magnetic phase transitions.
By the end of the module, students will develop a knowledge and understanding of magnetic and electric phenomena in condensed matter physics, in addition to an enhanced awareness of recent advances and current problems in condensed matter physics.

Computer Modelling
Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Java, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.
Students will develop a more thorough knowledge of the java language, including the use of inheritance, and will be able to write a physics modelling program in java.

Energy
The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative smallscale energy sources.
By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

Experimental Methods in Particle Physics
Students will study particle detection and experiments, exploring discoveries in particle physics and statistical tests, electroweak symmetry breaking and the Higgs mechanism. The module allows students to investigate CP violation and neutrino oscillations, and provides an introduction to supersymmetry and extensions to the standard model of particle physics.
By the end of the module, students will reinforce their knowledge and understanding of particle physics, and will gain a basic knowledge of experimental measurement and analysis techniques used in modern day particle physics research. Students will also develop an awareness of some recent advancements and current problems in particle physics research, and will go on to describe the successes and weaknesses of the standard model of particle physics and the possible theoretical extensions.

Flavour Physics
The module will cover various topics including CKM matrix and its parameterisations; unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current topics of heavy flavour physics, such as c and bhadron production and decay analysis, along with top quark physics.
Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector, neutrino oscillations and will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

Gauge Theories
The module covers various topics including Lagrangians and gauge transformations, global and local gauge invariance, gauge group and its representations and QED as a gauge theory. Students will explore QCD and nonabelian theories, asymptotic freedom and renormalisation group equation. The module discusses spontaneous symmetry breaking and Higgs mechanism, gauge structure of the electroweak theory, grand unified theories and extensions of the Standard Model.
By the end of the module, students will understand the modern phenomenology of the Standard Model of fundamental particles and will gain the mathematical background and physical insight into the fieldtheoretical structure of the Standards Model. Students will have an increased awareness of modern developments in Quantum Field Theory.

Groups and Symmetries
The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles.
By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

Lasers and Applications
This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing.
By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers. Students will understand the many uses of lasers in industry, medicine and the environment.

Matter at low temperature
The module begins by discussing what physicists mean by high and low temperatures, and looks at the different types of ordering that may occur as systems cool. Students will explore cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Students will observe the new phenomena that occur when systems are cooled below room temperature and will consider electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. The module provides an overview of the practical uses in superconducting quantum interference devices (SQUIDs).
The module seeks to explore a selection of fascinating phenomena that occurs when cooling matter to temperatures more than a million times colder than the familiar 290K of everyday life and observe the significance for both physics and technology. Additionally, students will appreciate the relation between temperature and order, will know how low temperatures are produced, including dilution refrigerators, and will also be able to describe the phenomena of superconductivity and superfluidity.

Physics of Fluids
Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.
Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the twofluid model of plasmas.
Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of NavierStokes equations, along with the wider applications of the NavierStokes theory to bio, geo and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

Physics of Living Systems
This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an informationprocessing system and the interactions between cardiovascular oscillations and brain waves.
Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.
Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then apply their knowledge of physics and mathematics to the understanding of basic principles of living systems – starting from a cell to the cardiovascular system and the brain.

Quantum transport in Low Dimensional Nanostructures
Students can expect to explore twodimensional electron systems, quantum transport in disordered lowdimensional electron systems and semiconductor quantum wires. The LandauerButtiker conductance formula is investigated, focusing on impurities in quantum wires, electronic transport in a magnetic field and the Hall effect. The module considers metallic point contacts, the pointcontact spectroscopy of the electronphonon interaction, and atomic breakjunctions and the scanning tunnelling microscope. Students will receive examples of applications of scanning tunnelling microscopy as part of the module.
By the end of the module, students will have knowledge of the physics of nanoscale solid state devices and how these may be manufactured and utilised. They will enhance their awareness of the recent advancements and current problems in condensed matter physics.

Semiconductor Device Physics
Students will familiarise themselves with crystal growth, including growth theory, faceting, impurity segregation and zone refining. The module presents students with a silicon case study, investigating semiconducting properties, silicon oxide, masking, surface pacification and photolithographic processing. Compound semiconductors will be discussed, covering band structure advantages over silicon, IIVI materials and effects of iconicity.
Additionally, students will explore thin film semiconductors, such as epitaxy, vapour phase growth, metalloorganic methods and liquid phase epitaxy, and the module provides a broad interdisciplinary overview of the linkage between the physics, chemistry and other materials sciences involved in the synthesis of semiconductors and the devices made from them.
By the end of the module, students will develop an understanding of the basic properties of crystals and crystal defects, and will be able to describe how crystals are grown and discuss the main semiconductor used for microelectronics as a detailed case study. Students will also demonstrate how physics continues to play a major role in enabling information technology.

SolarPlanetary Physics
Students will extend their knowledge on planetary systems, looking at the advances in planetary physics and planetary radiation environments. The module explores solarplanetary coupling and planetary magnetospheres, planetary magnetospheres within our solar system and unmagnetised bodies, such as Mars, the moon and comets. Students will study the heliosphere and beyond, investigating the sun’s influence on cosmic rays.
This module introduces students to the physical processes that dominate and characterise the planets in our solar system and those postulated to exist beyond. This will include the terrestrial planets, the outer planets and moons, the physics of planetary exploration, planetary astrophysics and the implications for life in the universe. Students will be required to carry out independent research on preset discussion topics and present their findings to the group in the form of oral presentations and posters in a series of seminars.
Students will be able to explain the key similarities and differences between the planets in the solar system, and will understand the role of a planet’s magnetic field in the retention of a gaseous atmosphere. Students will gain further skills such as the ability to calculate the scale size of a planet’s magnetosphere, and a developed knowledge of the important role of comparative planetology in our understanding of the solar system .In addition, students are required to undertake orbital mechanics calculations relevant to planetary systems and exploration.
Optional
Lancaster University offers a range of programmes, some of which follow a structured study programme, and others which offer the chance for you to devise a more flexible programme. We divide academic study into two sections  Part 1 (Year 1) and Part 2 (Year 2, 3 and sometimes 4). For most programmes Part 1 requires you to study 120 credits spread over at least three modules which, depending upon your programme, will be drawn from one, two or three different academic subjects. A higher degree of specialisation then develops in subsequent years. For more information about our teaching methods at Lancaster visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.

Basic Physics Skills / Communication Skills

Careers
Careers
Physics is an exciting subject that is fundamental to the developments in modern society. Applications of the subject range from the very pure to the very practical, and a physics degree opens up a wide range of rewarding careers in scientific research and technological development, as well as in a variety of other professions. A substantial number of our graduates continue on to postgraduate education, or enter employment that directly relies on their specialist skills. Our students also find employment in careers where they are valued because of general skills gained during the course such as logical thinking, problem solving, numeracy and computer literacy. Examples include consulting, finance, computer programming, and accountancy, as well as managerial and administrative positions.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability/career development, campus community and social development. Visit our Employability section for full details.

Fees and Funding
Fees and Funding
Fees
We set our fees on an annual basis and the 2019/20 entry fees have not yet been set.
As a guide, our fees in 2018 were:
UK/EU Overseas £9,250 £18,890 Channel Islands and the Isle of Man
Some science and medicine courses have higher fees for students from the Channel Islands and the Isle of Man. You can find more details here: Island Students.
Funding
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
Students taking Part I of the course are charged £10 for a bound copy of the lab manual. There are a number of optional oneday visits to places of interest and students pay travel costs.
Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.
The Department
10.3 hours
Typical time in lectures, seminars and similar per week during term time
44%
Average assessment by coursework
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