NATS6201: Teaching, Outreach and Public Engagement

• Terms Taught: Lent/Summer
• US Credits: 5 US Semester Credits 
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: None

PHYS4101: The Physical Universe

• Terms Taught: Michaelmas
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths AND physics

Course Description

This module will introduce the fundamental nature of Physics, and teach key skills in the use of experiment and uncertainty, units, and dimensional analysis. It will provide a foundation in topics such as Newton’s laws of motion, rotation of rigid bodies and the gravitational force. It will provide opportunities to apply some of these concepts to problems in physics and astronomy.

Educational Aims

Upon successful completion of this module students will be able to…

1. understand the nature and methods of physics
2. demonstrate knowledge and understanding of Newtonian mechanics, the kinematics and dynamics of rotation, rigid body, fluids and the gravitational force, and special relativity
3. explain a variety of physical and astronomical processes with the help of conservation laws, Newton's laws, kinetic and potential energy, angular momentum, moment of inertia and torque, and with gravitation and fluid dynamics
4. apply these basic physics principles to simple exercises and problems in physics and astronomy
5. collate and process information from different sources, including verbal information during a lecture, lecture notes and other sources (e.g. textbooks).
6. use a textbook and other learning materials to solve foundational exercises and problems.
7. apply knowledge to modelling real phenomena and situations.

Outline Syllabus

This module covers the nature of physics, the use of experiment and uncertainty, standards, units, significant figures, and dimensional analysis. It explores foundational concepts in classical and modern physics, beginning with motion in two dimensions, projectile trajectories, circular motion, and the rotation of rigid bodies. It delves into the dynamics of rotational motion, including torque and rotational energy, and study Newton’s laws alongside core ideas such as force, momentum, energy, and power. The principles of conservation, collisions, and impulse are examined, with an introduction to Lagrangian mechanics offering a modern analytical perspective. A key part of the module introduces Einstein’s theory of special relativity, covering simultaneity, time dilation, length contraction, and the Lorentz transformation. It further explores angular momentum, the moment of inertia, gyroscopic motion, and the role of the centre of mass. Topics in equilibrium, elasticity, and the mechanical properties of solids and fluids are also included. An astronomical perspective is included via a study of gravitation – from classical theories to black holes and dark matter – and the orbital motions of satellites and planetary bodies. Exoplanets are introduced as an example of pioneering discoveries, and methods of their detection are introduced to demonstrate applications of fundamental physics to frontier research.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Workshops are provided in which help is offered to students with questions on problem sets or other course content. Problem sets are regularly spaced across the module. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signaling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 30% weighting of the overall module credit.

The main summative assessment (70% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS4111: Mathematical Skills 1

• Terms Taught: Michaelmas
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths/physics

Course Description

This module aims to introduce students to fundamental mathematical concepts needed to model, describe and predict phenomena in the physical world. Students will learn mathematical techniques related to differentiation, integration, and complex numbers. The module will also provide students with opportunities to practice their mathematics skills, to develop their skills in solving problems, and to use mathematical modelling to describe the physical world.

Educational Aims

Upon successful completion of this module students will be able to…

1. recognise basic mathematical functions used in the description of physical phenomena, and their graphical representation.
2. differentiate basic functions directly, use systematic techniques to differentiate combinations of functions, find the stationary points of functions, and manipulate 3D vectors appropriately and use them to obtain directional derivatives.
3. Integrate basic functions of one variable directly, use systematic techniques to tackle more complicated integrals of one variable, and calculate important integrals over lines, areas and volumes.
4. describe and implement the principle of complex representation, manipulate complex functions, and obtain complex roots to equations.
5. use mathematical modelling and appropriate approximations to describe the physical world.
6. formulate problems in precise terms and to identify key issues.
7. collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

This module introduces fundamental mathematical concepts used to model, describe and predict phenomena in the physical world. Basic functions will be introduced, including periodic and trigonometric functions, exponential functions, natural logarithms, hyperbolic functions, polynomial functions, and the concept of inverse functions. Coordinate systems including 2D and 3D polar coordinates and coordinate transformations will be described, as well as vectors in Cartesian coordinates, the unit vector, the gradient vector, and the dot and cross products. Differentiation will be introduced from first principles using the notion of limits and methods of finding limits. Common techniques will be described to differentiate basic functions directly, as well as techniques to differentiate combinations of functions, such as the product, chain, sum and quotient rules. The concept of differentiation will be extended to consider logarithmic, parametric and implicit differentiation, partial and total differentiation, the extrema of graphs, tangent planes, linear approximations and directional derivatives. Methods will be discussed for finding maxima and minima of functions subject to constraints. Integration will be introduced as the area under a graph, and by the representation of definite integrals as the limit of a sum. The concept will be extended to include indefinite and improper integrals and integration techniques including simplification and integration by parts and by substitution. Applications in physics will be described with relation to integration over areas in Cartesian and polar coordinates, integration over volumes in different coordinate systems, parametric evaluation of integrals over lines. The integration of Heaviside function and delta-function will be described. Complex numbers will be introduced as represented by real and imaginary parts, and as points on the Argand diagram. Basic operations will be described including modulus, complex conjugate and rationalisation. The polar form of complex numbers and representation on the complex plane will be described and, via De Moivre’s theorem and Euler’s formula, the exponential form. The relation between trigonometric and hyperbolic functions and complex exponentials will be described. Complex functions and analytic functions will be introduced.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Workshops are provided in which help is offered to students with questions on problem sets or other course content. Problem sets are regularly spaced across the module. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 30% weighting of the overall module credit.

The main summative assessment (70% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS4151: Experimental Physics

• Terms Taught: Michaelmas
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths/physics

Course Description

This module aims to…

• Teach key skills in experimental physics and laboratory techniques at FHEQ level 4 and consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.
• Teach students relevant concepts in data analysis, problem solving and uncertainties.
• Explore simple AC circuits via application of electric and magnetic theory.
• Show how wave and oscillatory phenomena can be described mathematically.
• Illustrate physical principles described in lectures, and to develop skills of measurement and use of common instrumentation.
• Develop students' ability to use their initiative, be organised and meet deadlines.
• Give students experience interacting constructively with a colleague in a lab pair.

Educational Aims

Upon successful completion of this module students will be able to…

1. Assess the significance of experimental data through consideration of uncertainties and statistical analysis.
2. Calculate appropriate physical parameters describing a wave, recognise the wave equation, and solve it for a general situation.
3. Describe and explain universal wave phenomena such as interference, beats, and wave packets.
4. Describe and explain the behaviour of fundamental circuit components (battery, AC generator, resistor, capacitor, inductor).
5. Analyse quantitatively circuits containing resistance, capacitance and inductance to determine the behaviour of voltage and current in AC circuits.
6. Describe and explain the concept of resonance and the frequency dependence of reactance in designing simple filters.
7. Recognise a wide range of measurement instrumentation and use appropriate equipment to make measurements.
8. Perform simple analysis and presentation of data using appropriate computer software.
9. Perform a basic search of information via the internet (e.g. to find accepted values with which to verify their experimental results).
10. Appreciate the importance of uncertainties in experimental measurements.
11. Describe what constitutes a safe working environment.

Outline Syllabus

Lecture component: The lecture component of this module introduces students to topics that will be explored or applied in the laboratory. Systematic approaches to problem solving, assessing the validity of a solution, methods for the calculation and propagation of uncertainties will be introduced and applied to examples. Statistical analysis methods for data, the Normal (Gaussian) and Poisson distributions, will be described and applied. Topics in waves and oscillations will be explored, beginning with the simple pendulum, the physical pendulum and driven and damped harmonic motion. A mathematical description of waves will be introduced and used to understand general properties of waves such as speed, polarisation and energy flow. The Doppler effect, wave interference and normal modes will be introduced mathematically. Wave in gases and solids, standing waves, resonance, beats and wave packets will also be discussed. Revision of DC circuits. Alternating current (AC) generators and circuits, and combinations of resistance, inductance and capacitance will be introduced. Phasors and trigonometry, impedance, resonance, transformers and complex analysis of circuits will be described. Practical component: The practical part of this module will introduce the laboratory environment and computer graphical presentation of data. A set of introductory-level laboratory experiments will introduce basic experimental skills, log-keeping skills and familiarity with different scientific instruments and measurement techniques to allow the development of data taking, analysis and deductive reasoning skills. Errors or uncertainties will be introduced. The laboratory experiments will cover a range of physics topics including (but not limited to) waves, oscillations, identification of electrical components (resistor, capacitor, inductor), construction of circuits and AC circuit behaviour.

Assessment Proportions

Lecture material will be assessed via coursework in the form of pre-laboratory quizzes. The quizzes will require students to apply and consolidate their knowledge by solving previously unseen problems related to the laboratory session that will take place each week. Students will receive marks and feedback once the quiz has been submitted for grading. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 25% weighting of the overall module credit.

The main summative assessment (75% weighting) is related to the laboratory component of the module and will be split between continuous assessment using the logbooks completed during the lab sessions and a take home lab at the end of the module. Students will be expected to keep a log-book record during each laboratory session, which must be completed by the end of the 3-hour laboratory. Students will be given feedback on each logbook, including those that are not assessed. Three logbooks will be assessed for understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS4202: Fields, Matter and Quantum Physics

• Terms Taught: Lent/Summer
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths/physics

Course Description

This module will explore electricity, magnetism, thermodynamics, and quantum physics, providing a strong foundation in classical and modern physics. Through problem-solving and conceptual understanding, the module will provide opportunities for developing analytical skills applicable in physics, engineering, and research, application of mathematical models, understanding of physical principles, and interpretation of experimental results, essential for careers in scientific and technological fields.

Educational Aims

Upon successful completion of this module students will be able to…

1. demonstrate an understanding of the concept of a field; extend prior knowledge of the gravitational force to the concept of a conservative field; develop an understanding of the difference between a conservative field and non-conservative field
2. understand the basic concepts through which the phenomena of electricity and magnetism are described, in particular those of charge, current, field, and potential, and demonstrate knowledge and understanding of the laws governing electric and magnetic fields
3. demonstrate knowledge and understanding of thermodynamics, in particular the basic concepts of temperature, work, heat, internal energy and entropy and be able to explain the basic principles behind them
4. recognise that the ultimate description of the physical universe requires quantum, not classical mechanics; demonstrate a familiarity with a set of experiments which led to the breakdown of classical physics and hence; explain the basic ideas of wave mechanics, especially wave-particle duality, the probabilistic nature of quantum phenomena, and the uncertainty principle
5. apply the aforementioned physics principles to solving simple exercises and problems

Outline Syllabus

What connects lightning bolts, heat engines, and the strange dual nature of electrons? This dynamic module takes us on a journey through three pillars of physics – electromagnetism,?thermodynamics, and?quantum theory – revealing how they shape both the natural world and modern technology. We begin by exploring the invisible architecture of electric and magnetic fields. We’ll investigate how charges interact through Coulomb’s law, how fields store energy, and how moving charges create magnetic forces. From the force on a current-carrying wire to Faraday’s and Ampère’s laws, we’ll build a framework that underpins everything from electric motors to MRI machines. We’ll then investigate?thermal physics, starting with temperature, heat, and the Zeroth Law of Thermodynamics. We'll study energy flow, heat capacity, phase changes, and the equations of state, before tackling the First and Second Laws – covering concepts such as work, internal energy, entropy, heat engines, and the Carnot cycle. Finally, we plunge into the quantum realm, where particles behave like waves and measurement becomes a game of probabilities. Topics include the?photoelectric effect, atomic spectra, Bohr’s atom, and de Broglie’s matter waves. The module introduces Schrödinger’s equation and explores quantum ideas like tunnelling and energy quantisation in potential wells. This is not just a course in physics fundamentals – it’s a foundation for understanding how the universe works at every scale, from charged particles to cosmic radiation, from steam engines to quantum computers. Students will emerge equipped with both conceptual clarity and curiosity to explore further.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Workshops are provided in which help is offered to students with questions on problem sets or other course content. Problem sets are regularly spaced across the module. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signaling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 30% weighting of the overall module credit. The main summative assessment (70% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS4212: Mathematical Skills 2

• Terms Taught: Lent/Summer
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths/physics

Course Description

This module aims to introduce students to fundamental mathematical concepts needed to model, describe and predict phenomena in the physical world. Students will learn mathematical techniques related to series, differential equations, vector calculus, and the application of complex numbers to describe physical phenomena. The modules will also provide students with opportunities to practice their mathematics skills, to develop their skills in solving problems, and to use mathematical modelling to describe the physical world.

Educational Aims

Upon successful completion of this module students will be able to…

1. apply their knowledge of complex numbers and functions to describe phenomena involving phase and amplitude.
2. describe and use the representation of functions by series and approximations.
3. describe different types of differential equation and to solve separable 1st order and linear 2nd order differential equations.
4. extend elementary ideas of functions and calculus to a 3D description based on vector fields and potentials.
5. apply the concepts of divergence, gradient and curl to simple examples based on real physical phenomena.
6. use mathematical modelling and appropriate approximations to describe the physical world.
7. formulate problems in precise terms and to identify key issues.
8. collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

This module introduces fundamental mathematical concepts used to model, describe and predict phenomena in the physical world. Concepts of complex numbers will be extended to include the Fundamental Theorem of Algebra and roots of real polynomial equations, leading to an understanding of the roots of a complex number, roots of unity, reciprocals, and real and complex powers. The complex representation of harmonic waves will be introduced and applied to the solution of 1D damped oscillatory motion. The importance of differential equations for describing phenomena in the physical world will be discussed. Solutions of first order ordinary differential equations and second order ordinary differential equations with constant coefficients will be introduced, including methods for the solution of homogeneous and inhomogeneous second-order equations, auxiliary equation and trial solutions. Series, infinite series and series representations of functions will be described, including the summation of arithmetic, geometric and infinite geometric series, convergence tests, power series and radius and interval of convergence. Taylor expansions and Taylor polynomials will be introduced and applied to series representations of trigonometric and exponential functions. The concepts of functions and calculus will be extended to 3D descriptions based on vector fields and potentials. These descriptions will be related to examples from electromagnetism and quantum physics. The chain rule will be applied to real functions of many variables and used to introduce normal vectors and tangent planes to a 3D surface. The operations of gradient, divergence, curl and Laplacian will be introduced. The parametric representation of curves, surfaces and volumes will be described and applied to calculate lengths, areas and volumes. The representation of scalar and vector fields in spherical and polar cylindrical coordinates will be outlined. Line, surface and volume integrals will be introduced, including a discussion of the Jacobian. Gauss’s theorem and Stokes’ theorem will be described and illustrated using examples from electromagnetism.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Workshops are provided in which help is offered to students with questions on problem sets or other course content. Problem sets are regularly spaced across the module. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 30% weighting of the overall module credit.

The main summative assessment (70% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS4252: Physics Skills

• Terms Taught: Lent/Summer
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: A level (or equivalalent) grade A maths/physics

Course Description

This module is designed to develop fundamental skills in data analysis, scientific communication, and computational techniques. Additionally, students will learn about ethical scientific working and career preparation. These are core skills for a physicist, introduced at level 4 to address accreditation requirements and provide a foundation for study at level 5 and beyond.

Educational Aims

Upon successful completion of this module students will be able to

1. synthesise scientific knowledge and construct arguments in a succinct and concise manner using technical language
2. describe how to communicate scientific ideas to a range of audiences
3. appropriately cite scientific literature
4. describe the standard structure of a scientific report and know how to use a mark-up language (such as LaTeX) to write a formal scientific report
5. prepare and present efficiently a presentation
6. appreciate what constitutes ethical programming including the roles and responsibilities that technical programmers have in a research and industry setting
7. write a piece of code to fit experimental data of an arbitrary nature
8. demonstrate self-awareness of personal skills, motivations and development needs
9. identify and investigate available and relevant career opportunities and demonstrate the ability to apply effectively for jobs and other opportunities
10. demonstrate an appreciation of ethical considerations in science and the appropriate ethical frameworks.
11. demonstrate an appreciation of intellectual property, and environmental and sustainability issues.
12. appreciate basic concepts of astronomical measurements and apply them in calculations

Outline Syllabus

Scientific writing skills will be introduced, including the structure of a formal scientific report, planning and delivering a concise argument, preparation of a report in LaTeX or similar mark-up language and appropriately citing references. To complement this research skills of library use, literature searching and summarising sources will also be taught. These will be practiced and developed in the preparation of a report. Methods of communication and knowledge exchange will be discussed including written articles, oral presentations, audio and visual media, with consideration of their use in outreach. Principles of oral and poster presentations, their preparation and delivery will be taught and put into practice. Programming and scripting basics will be introduced and practiced, such as, running simple programs, importing modules, variable types, input and output, and mathematical functions.?The important process of debugging will be explained, for example, the identification and classification of programming errors. The basic application of programming to data analysis and plotting methods will be introduced and practiced such as, line plots, histograms, error bars, time-series analysis, linear and curve fitting. Basic concepts of astronomical measurements will be introduced, such as luminosity, distance, blackbody spectra and telescopes and instrumentation. Important professional skills for a physicist will be taught. Career destinations and opportunities will be reviewed and tools to assist in finding jobs and guiding professional development will be identified. CV preparation and expectations will be covered. The expectations of ethical and inclusive behaviour and practices in science will be taught, including plagiarism, with reference to the IOP code of conduct. Students will be given an appreciation of intellectual property considerations, and environmental and sustainability issues.

Assessment Proportions

Coursework is designed to consolidate student learning and assess the wide-ranging learning outcomes.

• Coursework (40%) will be regularly spaced across the module. The coursework complements both the lectures and workshops with feedback to the class and/or individual feedback offered. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback.
• The report (40%) assesses both communication and report writing skills and application of coding skills in the plotting and fitting of data and the preparation of a formal report.
• The presentation (20%) assesses communication and presentation preparation skills.

PHYS5053: Introduction to Experimental Laboratories

• Terms Taught: Full Year
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: Introductory university level physics and maths

Course Description

This module is aimed at undergraduate students not studying for a Physics degree and is essential for any such students wishing to take practical or project modules in the Physics Department at level 5, 6 or 7. The module is designed to introduce essential experimental skills and techniques through a range of individual experiments drawn from various topics in physics, complemented by lectures. It teaches techniques of experimental data collection and analysis, ethical standards in a scientific investigation and health and safety. Students are taught and apply the general and IT skills required for the manipulation and presentation of data, logbook and report writing.

Educational Aims

Upon successful completion of this module students will be able to

1. use a range of experimental equipment to conduct measurements and exhibit a practical experience of experimental methods
2. collect experimental data using a variety of common instruments
3. perform a statistical assessment of the validity of experimental observations, their uncertainties and the validity of their model interpretation
4. show a working knowledge of the basic principles DC and AC circuit analysis, transient response and resonance in mechanics and electric circuits
5. apply physics knowledge and problem-solving skills to problems in science
6. systematically record their work in a log book
7. report their results in written and oral form
8. employ general and IT skills required for the manipulation and presentation of data, log book and report writing
9. discuss the role of health and safety in scientific experimentation and demonstrate high ethical standards during a scientific investigation.

Outline Syllabus

This module includes laboratory work and complementary lectures, to introduce and develop essential practical and investigatory physics skills. A range of foundational physics experiments will be undertaken, drawn from multiple physics fields, including optics, atomic physics, quantum physics and electronics. Possible experiments include spectroscopic measurement of emission from hydrogen atoms; characterisation of electrical transients; studying radioactive decay and the nature of beta and gamma particles; the photoelectric effect and measuring the fundamental electron charge. A laboratory manual is provided, to introduce the background if each experiment and guide the students as they assemble apparatus and complete the investigations. The experiments are designed to develop practical skills with a range of laboratory equipment, including oscilloscopes, spectrometers and various meters. Demonstrators will discuss the work with students during the lab, helping them learn how to operate the equipment. Lectures and online asynchronous learning teach the basic concepts of statistical analysis of data and uncertainties, ethical behaviour, the role of health and safety in scientific experimentation, IT skills including the preparation of documents and data plots, and the basic principles of DC and AC circuit analysis, transients and resonance in the context of mechanics and electrical circuits. Practical and investigatory physics skills developed include making measurements, assessing errors and uncertainties, systematic and random errors, recording data, keeping log books, propagation of uncertainties, statistical analysis of data, normal (Gaussian) and Poisson distributions. Complemented by an understanding of the role of health and safety in scientific experimentation, ethical behaviour in science and plotting and report preparation skills. The important transferable skills of written and oral communication are developed and practiced through the preparation of a formal report and the delivery of a presentation.

Assessment Proportions

The module convenor will be present during the lab sessions to oversee safety. The students work in pairs or small groups to conduct experiments. The convenor and supporting demonstrators regularly check on progress, provide feedback for formative assessment, and help with problems or questions. Practical skills are developed thorough guidance and demonstration. The continuous laboratory assessment takes the form of an electronic log book – a contemporaneous account of the work of each student. The module convenor checks the log book periodically throughout the lab to provide formative assessment and provide written feedback. Log books are periodically marked for summative assessment. Lectures and online content teach the basic concepts of statistical analysis of data and uncertainties, distributions and regressions, ethical behaviour, the role of health and safety in scientific experimentation, IT skills including the preparation of documents, and the basic principles of DC and AC circuit analysis, transients and resonance in the context of mechanics and electrical circuits. Coursework assignments practice and develop understanding. Assessment consists of a continuous lab assessment element (30%), worksheets (10%) a presentation (20%) and a report (40%).

PHYS5054: Experimental Physics, Mechanics and Symmetry

• Terms Taught: Full Year
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: Introductory university level physics and maths

Course Description

This module aims to…

• Teach an overview of theoretical methods used in classical mechanics building on content from FHEQ level 4, consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.
• Introduce group theory, enabling students to sit relevant mathematics modules at levels 6 and 7.
• Provide students with the opportunity to practice relevant mathematics skills and to develop their skills in solving problems in classical mechanics.
• Provide an introduction to key skills in experimental physics and to transferable and professional skills.

Educational Aims

Upon successful completion of this module students will be able to…

1. Explain how concepts of the variational principle and symmetry may be applied to describe and understand classical mechanics.
2. Apply the variational principle to solve problems in classical mechanics.
3. State basic definitions in the theory of groups, such as those of a subgroup or a homomorphism, provide multiple examples of each and prove basic results about them.
4. Demonstrate understanding of the application of groups and group theory to the study of symmetries of mathematical objects, and carry out computations in specific examples such as matrix groups.
5. Perform independent and self-directed learning, and demonstrate analytic skills by paying attention to detail, describing advanced concepts using logical arguments and correct technical language. Be able to formulate problems in precise terms and identify key issues.
6. Demonstrate skills related to experimental measurements including working co-operatively with colleagues, use of appropriate equipment, data collection and presentation, recording work in a log book, and understanding the role of health and safety in scientific experimentation.
7. Write a technical, scientific report using appropriate software, adhering to ethical principles, transparency, and avoiding bias or plagiarism. Perform a statistical assessment of the validity of experimental observations and the validity of their model interpretation.
8. Demonstrate an appreciation of ethical scientific behaviour and of the importance of equality, diversity and inclusion in professional activities. Recognise intellectual property, environmental, and sustainability issues in the context of theoretical physics and mathematics, and evaluate the broader impact of physics, mathematics and Lancaster University locally and globally.

Outline Syllabus

This module provides an overview of theoretical methods used in classical mechanics, describing Newton's laws of motion with emphasis on central forces, dynamics and orbits, and integrals of motion. Other examples include one-dimensional dynamical problems such as linear and non-linear oscillators. The module introduces the least action principle, the Lagrangian, and Lagrange's equations of motions, giving their relation to Newton's laws of motion. Concepts described include symmetries and conservation laws; generalised coordinates and momenta; the Hamiltonian and Hamilton's equations of motion. The section on group theory will cover the abstract theory of groups, including groups, subgroups, cosets, orders, normal subgroups, Lagrange's theorem and the first isomorphism theorem. Various families of examples will be explored, including matrix groups and symmetry groups of geometric objects. Some group actions will be explored via examples. There is an introduction to experimental practical laboratory and essential physics skills. Lectures cover the basic concepts of statistical analysis of data and uncertainties, ethical behaviour, the role of health and safety in scientific experimentation, IT skills including the preparation of documents, intellectual property, environmental and sustainability issues in the context of experimental physics, and the societal impact of physics and mathematics and of a Lancaster degree in Theoretical Physics with Mathematics. There are three 3-hour laboratory sessions, where students perform experiments in optics, mechanics and electric circuits which illustrate and complement the taught material. At the end of the laboratory sessions, students are required to write a scientific report on one of the experiments. Laboratory sessions focus on basic experimental skills including making measurements, assessing errors and uncertainties, recording data and keeping log books, and report writing. Physics teaching will align with the Institute of Physics Degree Accreditation Framework Principle requiring institutions to have a clear commitment to equality, diversity and inclusion in the physics curriculum. This will be enabled via resources developed within the IOP’s Inclusive Physics Curriculum project, which includes material highlighting the diversity of people who have contributed to physics and exploring some of the historical context around how physics knowledge has been constructed in the fundamental areas of physics which must be covered in an IOP accredited physics curriculum.

Assessment Proportions

• Periodic problem sets (20%)
• Exam (60%)
• Logbook (10%)
• Report (10%)

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the course with two to three week gaps, minimising competing deadlines in concurrent lecture modules. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit to encourage student engagement with the coursework and to provide variety in the module assessment. The main summative assessment (60% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions. Such controlled conditions are essential to ensure the validity and integrity of the assessment for this subject. For the practical laboratory, each student undertakes a separate experiment every week. During the experiment, they complete a log book which is submitted for marking when the lab session has ended (10% weighting). It is returned with written feedback by the beginning of the next week's lab session. Accompanying lectures teach essential laboratory and physics skills which are tested with a problem set. At the end of the laboratory sessions, students complete a scientific report (10% weighting) about one of the experiments. It is marked and returned with written feedback

PHYS5101: Electromagnetism, Waves and Optics

• Terms Taught: Michaelmas
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: University level introductory electromagnetism and maths

Course Description

This module will build on the FHEQ level 4 content covered in module PHYS4202 (or equivalent) to provide a deeper understanding of electromagnetism, electromagnetic waves and their propagation, and of simple optical instruments. It will provide students with the opportunity to practice relevant mathematics skills and to develop their skills in solving problems in electromagnetism, waves and optics. It is being offered for consistency with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.?

Educational Aims

Upon successful completion of this module students will be able to…

1. demonstrate the use of vector calculus and Maxwell’s equations in describing electromagnetic phenomena;
2. describe electromagnetic fields and waves in different media;
3. describe geometrical optics, diffraction and interference phenomena and give examples of instruments exploiting these phenomena.
4. describe the basic elements of a laser, laser operation and important features of laser light.
5. apply their physics and mathematics knowledge and problem-solving skills to describe advanced topics

Outline Syllabus

This module provides a broad and integrated introduction to electromagnetism, wave physics, and optics, building on core principles to develop a deeper understanding of how electric and magnetic fields interact and propagate. The module begins by revisiting the Lorentz force, and the key mathematical tools needed to describe physical fields, electrostatics (the behaviour of charges, electric potentials, and the influence of materials such as conductors and dielectrics) and magnetic fields (including the Biot-Savart law, and inductance). With these foundations in place, the module develops toward a full formulation of classical electromagnetism through Maxwell’s equations, exploring both their differential and integral forms, and their implications for the energy and momentum carried by electromagnetic fields. Students will investigate how these equations give rise to electromagnetic waves, and how such waves propagate through different media, reflect and refract at boundaries, and are guided by structures like waveguides and coaxial cables. The latter part of the module focuses on the physics of waves and optics. After reviewing geometrical optics, the course addresses the behaviour of light as a wave, including interference, diffraction, and polarisation. Concepts such as coherence, resolution, and the performance of optical instruments are examined, with practical examples including cameras and interferometers. Finally, the module introduces the physics of lasers, exploring how coherent light is produced and what makes laser light unique, providing insight into a powerful application of electromagnetic wave theory.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the course. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signaling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit to encourage student engagement with the coursework and to provide variety in the module assessment.?? The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions. Such controlled conditions are essential to ensure the validity and integrity of the assessment for this subject.

PHYS5111: Mathematical Techniques in Physics

• Terms Taught: Michaelmas
• US Credits: 5 US Semester Credits
• ECTS Credits: 10 ECTS Credits
• Pre-requisites: University level introductory maths

Course Description

This module aims to develop students’ knowledge and understanding of advanced mathematical concepts needed to model, describe and predict phenomena in the physical world. Students will learn important techniques from linear algebra and become familiar with the concepts of Fourier series and Fourier transforms. The module will also provide students with opportunities to practice their mathematics skills, to further develop their skills in solving problems, and to use advanced mathematical techniques to describe complex physical phenomena.

Educational Aims

Upon successful completion of this module students will be able to…

1. solve problems involving systems of coupled linear equations.
2. understand and apply common matrix manipulations.
3. solve common types of linear equations, such as the wave equation in 3D, using Cartesian, cylindrical and spherical polar coordinates.
4. express periodic functions as Fourier series and find the Fourier transform of functions.
5. solve differential equations and describe physical phenomena using Fourier techniques.
6. apply advanced mathematical techniques to describe the physical world.
7. formulate problems in precise terms and to identify key issues.
8. collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

This module introduces advanced mathematical concepts used to model, describe and predict phenomena in the physical world. Solutions of the wave equation with boundary conditions in 1D, 2D and 3D will be described. The concepts of a basis function, orthogonality of harmonic functions, completeness of a basis and the Kronecker delta will be introduced. The Laplace operator in Cartesian, cylindrical and spherical coordinates will be introduced. Angular harmonics in 2D and Spherical harmonic functions in 3D will be discussed, including the relation between plane waves, cylindrical waves and Bessel functions. Linear algebra techniques will be introduced and used to solve systems of coupled linear equations and systems of linear ordinary differential equations. The concepts of the determinant of a matrix, eigenvalues and eigenvectors, diagonalisation of matrices and commutation relations involving matrices will be described. Symmetric and Hermitian matrices will be introduced, including methods for their diagonalisation using orthogonal and unitary matrices. Fourier series representations of periodic functions will be introduced, including examples of real and complex Fourier series. Parseval’s theorem will be discussed and related to physical examples. Fourier series will be applied to physical systems with forced oscillations and dissipation, including mechanical and electrical systems. The concepts of the Fourier transform and the inverse Fourier transform will be defined, leading to the expression of a function as a Fourier integral. The integral representation of the Dirac delta-function will be introduced. Fourier transforms will be used to find general solutions of the wave equation and to solve the 1D wave equation with initial conditions (d’Alembert’s solution). The convolution of two functions and its connection with Fourier transforms will be discussed. Boundary and initial condition problems will be described through examples including the diffusion equation, the heat equation and applications in electrostatics. Laplace’s equation and the Uniqueness Theorem will be introduced, and time-dependent solutions with initial conditions and solutions for arbitrary boundary conditions will be described.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the course. The problem sets are marked and returned with feedback to students within approximately one week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit to encourage student engagement with the coursework and to provide variety in the module assessment. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions. Such controlled conditions are essential to ensure the validity and integrity of the assessment for this subject.

PHYS5151: Physics Modelling Project

• Terms Taught: Michaelmas
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Introductory level coding (e.g. Python)

Course Description

This module aims to enable students to...

• Employ fundamental concepts underlying many computer languages and apply them to numerical problems.
• Evaluate computational techniques and appraise their effectiveness.
• Design and implement a simulation of a complex system using advanced programming techniques and analyse the results.
• Enhance their skills in problem solving and writing critical reports.
• Gain an understanding of how simulated data may be generated and analysed, both qualitatively and quantitatively.
• Practice working independently.
• Reinforce concepts of ethics in science, academic honesty and ethical programming.

Educational Aims

Upon successful completion of this module students will be able to…

1. Write, design and test computer programs that can be used for numerical simulation and data analysis.
2. Employ appropriate computational and programming techniques to model simple physical systems.
3. Identify relevant principles and laws when dealing with problems, and make approximations necessary to obtain solutions.
4. Understand numerical precision and accuracy.
5. Compare the results of a model calculation with experimental data or observations.
6. Plan, manage and independently complete an open-ended project to model a physics-based problem.
7. Formulate appropriate conclusions and present them in a written scientific report.
8. Demonstrate an appreciation of ethical considerations in science, academic honesty and ethical programming.

Outline Syllabus

This module will introduce basic programming techniques including writing and running simple programs, types of variables, mathematical functions and input and output. Methods for debugging programs and identification and classification of programming errors will be demonstrated. Iterative methods such as “for”, “while” and nested loops and methods such as arguments and signatures will be introduced. Numerical approximations such as the Euler method and numerical algorithms will be used in programs that solve numerical problems and/or model physical systems. Object orientated programming, class design, class testing and documentation will be introduced. Objects and methods will be used to represent physical systems. Code development infrastructure, which may include code repositories, testing and other technologies, data visualisation and analysis techniques will be described. Students will undertake a modelling project where they will write a numerical program to model a physical system and/or address a problem in an area relevant to their chosen degree scheme. Academic honesty, ethical behaviour and ethical programming will be discussed and the principles applied to the modelling project.

Assessment Proportions

Lecture material will be assessed via coursework in the form of introductory exercises. These exercises will require students to apply and consolidate their knowledge by applying computational methods to unseen exercises. The coursework is marked and returned, with feedback provided to students via feedback sessions within approximately one week of submission, to ensure regular and timely signalling to them. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The introductory exercises are given a 30% weighting of the overall module credit.? The main summative assessment (70% weighting) is a portfolio consisting of a written report and the student’s code used to address the given problem.

PHYS5202: Quantum Mechanics and Atomic Physics

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: University level introductory quantum physics and maths

Course Description

This module aims to… Teach the fundamentals of quantum mechanics, building on content from FHEQ level 4, with applications to atomic physics, consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework. Provide students with the opportunity to practise relevant mathematics skills and to develop their skills in solving problems in quantum mechanics and atomic physics.

Educational Aims

Upon successful completion of this module students will be able to…

1. Apply quantum mechanics and mathematics to simple, exactly solvable problems using the Schrödinger equation.
2. Systematically find approximate solutions for quantum systems that are not exactly solvable.
3. Demonstrate that quantum mechanics can be used to describe the ground and excited states of atoms, apply quantum mechanics to transitions between atomic states, and explain the origin of selection rules.
4. Formulate problems in precise terms and identify key issues.
5. Collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

Concepts of quantum mechanics will be developed through applications of the Schrödinger equation to one-dimensional systems including a particle in an infinite square well; piecewise constant potentials; the harmonic oscillator; and notions of bound states, the ground state, zero-point energy, tunnelling and resonance. This will be accompanied by a revision of essential mathematics for quantum mechanics including differential equations, calculus and linear algebra. Axioms and advanced mathematics of quantum mechanics will be introduced including states as vectors (and the superposition principle); Dirac notation; time dependence; observables as operators; associated linear algebra and functional analysis (eigenvalue problems, Fourier analysis); probabilities and expectation values; commutation relations; uncertainty principle; and the comparison to classical mechanics. The use of time-independent perturbation theory for analytically intractable problems is described. Applications to three-dimensional systems include a 3d particle in a box; the 3d harmonic oscillator; angular momentum; the hydrogen atom; quantum numbers and level degeneracy. Applications to spin include spins and electrons in magnetic fields, and the Stern-Gerlach experiment; and the Zeeman effect. Time-dependent problems are introduced using the time-dependent Schrödinger equation, the time-evolution operator, and the Ehrenfest equations of motions. Applications include wave packet dynamics of the free particle and in the harmonic oscillator, spin precession, and Rabi oscillations. Electronic transitions between states are described using time-dependent perturbation theory including Fermi's golden rule, transition matrix elements, parity and selection rules. Many particle systems are described using the Pauli principle and the concept of bosons and fermions. The application of quantum mechanics to atomic physics is described through the periodic table of elements; the spin-orbit magnetic interaction, and the fine and hyperfine structure of atomic levels. . Atoms with more than one electron in the outer shell are described using appropriate approximations.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS5203: Properties of Matter

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: University level introductory thermal physics and maths

Course Description

This module aims to develop students’ knowledge and understanding of thermodynamics and the macroscopic properties of matter, and to use concepts from statistical physics to relate macroscopic properties to the microscopic world. The module will provide students with the opportunity to practice relevant mathematics skills and to develop their skills in solving problems in thermal and solid-state physics.

Educational Aims

Upon successful completion of this module students will be able to…

1. Understand and apply thermodynamic potentials and associated thermodynamic relations to describe thermal behaviour.
2. Apply statistical concepts to explain the properties and behaviour of macroscopic systems.
3. Demonstrate an understanding of the mechanical, electrical, magnetic and thermal properties of matter and the microscopic origins of these properties.
4. Formulate problems in precise terms and identify key issues.
5. Collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).?

Outline Syllabus

This module introduces and develops the topics of thermodynamics and statistical physics and explores the connections between microscopic structure and macroscopic properties of matter. The module will review the fundamental concepts of temperature, equations of state, thermodynamic cycles and the zeroth, first and second laws of thermodynamics. The concept of entropy will be explored, leading to a description of the thermodynamic potentials. The Clausius-Clapeyron equation will be introduced, and the nature and classification of phase transitions described. The microscopic structure of solids will be explored to explain why different solids exhibit different mechanical, electrical, magnetic and thermal properties. This will include a discussion of crystals, lattices and atomic basis. Phonons will be introduced as lattice vibrations, including a description of phonon dispersion relations and the differences between optical and acoustic modes. The Drude model will also be introduced to describe charge transport in conductors, the Wiedemann-Franz law and the Hall effect. The connection between thermodynamics and statistical mechanics will be introduced by comparing microscopic and macroscopic pictures, and introducing microstates and macrostates, partition functions, the Boltzmann distribution and the Boltzmann-Planck equation. Statistical properties of solids will be described via 2-level systems to show, in more detail, how macroscopic properties of matter such as heat capacity and ferromagnetism emerge from microscopic behaviour such as lattice vibrations and spin interactions. Further concepts from statistical physics will be introduced, including the density of states, particle statistics, and the behaviour of Maxwell-Boltzmann gases and Fermi-Dirac gases. This will lead to a broad discussion of macroscopic properties of matter that includes more exotic behaviour such as Bose-Einstein condensation and superfluidity.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit.?? The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS5252: Experimental Labs

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: University level introductory experimental / introductory laboratory physics

Course Description

This module is designed to develop experimental skills and techniques through a range of individual experiments drawn from various topics in physics, including particle physics. Many experiments complement the physics topics taught in other level 5 modules. Experimental and investigative skills will be developed beyond those introduced at level 4, with students learning to handle more complex experiments and result analysis. The module prepares students for experimental physics at level 6. The module is offered as core component of our Physics programme and is consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.

Educational Aims

Upon successful completion of this module students will be able to

1. use a range of experimental equipment to conduct measurements
2. identify, estimate, combine, minimise and quote experimental errors
3. critically analyse and interpret experimental results
4. perform a statistical analysis
5. maintain a contemporaneous record of their work that includes their approach, results and conclusions
6. write a formal report that presents the results of an experimental investigation, draws appropriate conclusions and cites the published literature to compare results to the field
7. prepare and deliver a scientific presentation

Outline Syllabus

In this module students will undertake a range of experiments giving them firsthand experience of some core physical phenomena and properties. Experiments are drawn from a range of physics fields, including optics, atomic physics, quantum physics, particle physics and electronics. Possible experiments include the measurement of the angular distribution of cosmic rays; the measurement of momentum conservation in positronium decays; characterisation of single photon diffraction; blackbody radiation and the Stefan-Boltzmann law; Fourier analysis using filters; Spectroscopic measurement of emission from atoms. A laboratory manual is provided, to introduce the background if each experiment and guide the students as they assemble apparatus and complete the investigations. The experiments are designed to develop practical skills with a range of laboratory equipment, including oscilloscopes, spectrometers and various meters. Demonstrators will discuss the work with students during the lab, helping them learn how to operate the equipment. The important transferable skills of written and oral communication are developed and practiced through the preparation of a formal report and the delivery of a presentation.

Assessment Proportions

Assessment consists of a continuous element (50%) a presentation (20%) and a report (30%). The continuous element takes the form of an electronic log book – a contemporaneous account of the work of each student. The module convenor checks the log book periodically throughout the lab to provide formative assessment and provide written feedback. Log books are periodically marked for summative assessment.?? During the module the students will deliver a presentation providing summative evaluation of their oral communication and formative feedback on their data analysis. Towards the end of the module students will complete a report. Students will be able to discuss feedback on their earlier work on their chosen report subject and get feedback on their planned report structure. Students will be able to complete their reports outside of the lab, including conducting some review of the literature to place their results into context.

PHYS5261: Stellar and Nebular Astrophysics

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Introductory university level physics and maths

Course Description

In this module, student will learn about the structure and life cycle of stars, as well as their formation within and interactions with their local environments. This will include an introduction to radiative transfer as it applies to the interstellar medium and stellar interiors, formation and evolution timescales in multiple stellar and nebular contexts, and coverage of the key factors driving the formation, structure and evolution of stars at different masses. By studying the end-to-end life cycle of stars of all types, as well as the environments in which they form, live and die, students will develop an understanding of the processes that give rise to the objects we observe across the universe. Concepts from quantum, nuclear, particle, condensed and relativistic physics will be applied to explain the stellar remnants at the end of a star’s life such as white dwarfs, neutron stars and black holes.?

Educational Aims

Upon successful completion of this module students will be able to…

1. Apply physical principles and mathematical models to analyse the internal structure of stars and interpret stellar behaviour using the equations of stellar structure and fundamental laws of physics.
2. Explain and evaluate the processes governing stellar evolution across different mass ranges, including the formation and characteristics of stellar remnants such as white dwarfs, neutron stars, pulsars, and black holes.
3. Interpret observational and theoretical evidence to analyse stellar phenomena, including Hertzsprung-Russell diagrams, binary systems, mass transfer mechanisms, and accretion processes.
4. Demonstrate broad knowledge of the physical properties of stars and nebulae and the observational techniques used to determine them.
5. Explain the fundamental physical principles governing stellar stability, energy generation, and energy loss in stars and nebulae.
6. Apply physics to solve problems related to star formation, gravitational collapse, main sequence stability, and stellar evolution.

Outline Syllabus

This module provides a comprehensive exploration of stellar astrophysics, examining the physical principles that govern the structure, formation, and evolution of stars. Beginning with the foundational equations of stellar structure, students will subsequently study polytropic models, the Lane-Emden equation, and numerical techniques used to construct stellar models, including the use of Kippenhahn diagrams. The course delves into the physics of thermonuclear fusion, covering key processes such as the proton-proton chain, CNO cycle, triple-alpha process, and helium burning, as well as the role of quantum tunnelling, reaction cross-sections, and the Gamow peak in determining fusion rates. Students will investigate the evolutionary pathways of stars in-depth, from the main sequence through the red giant and asymptotic giant branches for low and intermediate mass stars, to planetary nebulae and white dwarf formation, and the evolution of massive stars through successive nuclear burning phases to core collapse supernovae and gamma-ray bursts. Students will also investigate binary systems, accretion processes, and the physics behind Type Ia supernovae and compact object jets. Pulsars and neutron stars are studied through their observable properties, spin-down mechanisms, and gravitational wave emission in binaries. A section on black holes covers the Schwarzschild metric, event horizons, and observational evidence including gravitational lensing. The course also reviews measurable stellar properties—mass, luminosity, spectra—and their depiction on the Hertzsprung-Russell diagram. Students will explore formation processes, from molecular cloud collapse governed by the Jeans criterion to protostar development and entry onto the main sequence, alongside timescales relevant to the interstellar medium, stellar life cycles, and energy transport mechanisms in stellar interiors.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students, normally within a week of submission, to ensure regular and timely signaling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS5271: Mechanics, Variations and Symmetry

• Terms Taught: Lent/Summer
• US Credits: 5 
• ECTS Credits: 10 ECTS
• Pre-requisites: Introductory university level physics and maths

Course Description

This module aims to…

• Teach an overview of theoretical methods used in classical mechanics, and introduce group theory, building on content from FHEQ level 4, consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.
• Provide students with the opportunity to practice relevant mathematics skills and to develop their skills in solving problems in classical mechanics.

Educational Aims

Upon successful completion of this module students will be able to…

1. Explain how concepts of the variational principle and symmetry may be applied to describe and understand classical mechanics.
2. Apply the variational principle to solve problems in classical mechanics.
3. Describe elementary group properties and apply group theory to problems in physics.
4. Formulate problems in precise terms and identify key issues.
5. Collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

This module provides an overview of theoretical methods used in classical mechanics. The module describes Newton's laws of motion with emphasis on central forces, dynamics and orbits, and integrals of motion. Other examples include one-dimensional dynamical problems such as linear and non-linear oscillators. The module introduces the least action principle, the Lagrangian, and Lagrange's equations of motions, giving their relation to Newton's laws of motion. Concepts described include symmetries and conservation laws; generalised coordinates and momenta; the Hamiltonian and Hamilton's equations of motion. Group theory is presented including the definition of a group, conjugates and classes, subgroups, symmetry and transformations, and irreducible representations. Characters of finite groups are described including orthogonality relations for characters and character tables. The module also introduces Lie groups including generators, and orthogonal and unitary groups. Throughout the module, examples in physics are used to illustrate abstract concepts, and students develop skills in applying the taught methods through problem sets.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS6051: Industrial Group Project

• Terms Taught: Full Year
• US Credits: 10
• ECTS Credits: 20 ECTS
• Pre-requisites: Intermediate level university physics and maths. Students either take PHYS6152+PHYS6254 OR PHYS6051

Course Description

This module is designed to give students the opportunity to apply their physics knowledge and skills, obtained at levels 4, 5 and 6, to an industry-motivated project. This requires them to develop and apply analytical and problem-solving skills in a context where there is no pre-determined method. The modules aims to develop transferable skills beyond those already obtained at level 5, including teamwork, problem-solving, time- and project-management, and communication skills. The module is offered as an optional component of our Physics programme and is consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.

Educational Aims

Upon successful completion of this module students will be able to

1. apply their physics knowledge to open-ended, industrially-oriented problems
2. investigate an area of physics in a systematic way using appropriate techniques and equipment
3. systematically record their work in a logbook
4. work successfully in a team to tackle large-scale problems
5. effectively communicate their work, both in writing and orally, sharing insights and drawing appropriate conclusions

Outline Syllabus

A module handbook is provided, to summarise the structure and expectations of the module, and to provide useful information to support the project work. At the beginning of the module, students will be taught about the fundamentals of project management, further supported by the project manual. They will then put this knowledge into practice to plan, assign and complete the project work. Students will draw on their broad physics knowledge and approach to problem solving and practical work, to addressing the subject of their “real life” project. Essential skills for generalist article writing and a general introduction to oral dissemination of scientific concepts will be taught and developed at a workshop. Oral presentations will be delivered by students and formally assessed by staff at the physics undergraduate conference (The PLACE - The Physics @ Lancaster Annual Conference & Exhibition).

Assessment Proportions

Assessment consists of a final individual report (50%); group work and continuous assessment (30%) via a logbook, planning document and convenor observation; a viva (10%); and a presentation (10%). The planning document, submitted during the first half of the module, and oversight of the contemporary log-books, allow the convenor(s) to monitor the progress and direction of work, supported by discussion in the weekly lab sessions and student presentations in workshop sessions. Student will be able to get feedback on their planned report structure and complete their reports outside of the lab.

PHYS6109: Properties of Materials and Particles

• Terms Taught: Michaelmas
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Intermediate level university physics and maths.

PHYS6152: Low Temperature & Semiconductor Laboratory

• Terms Taught: Michaelmas
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: University level introductory experimental / introductory laboratory physics

Course Description

This module is designed to explore the interesting physics of both semiconductors and matter at low temperature through a series of experimental investigations. By characterising devices and experimental samples across a range of temperatures, students study physical phenomena related to thermodynamics, statistical physics, and quantum mechanics introduced at level 5. Experimental and investigative skills will be developed beyond those obtained at level 5, with greater independence in planning and managing the work. The module prepares students for experimental physics projects at level 7. The module is offered as an optional component of our Physics programme and is consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.

Educational Aims

Upon successful completion of this module students will be able to

1. demonstrate use of a range of advanced experimental equipment, including optical and cryogenic apparatus, to plan and conduct physical measurements
2. analyse and interpret experimental results in relation to the theories and laws of condensed matter physics
3. identify and examine the properties of superfluids and superconductors
4. apply the concepts of band theory to analysing optical and electronic properties of semiconductors
5. work effectively with colleagues to achieve a common goal, solve problems and obtain results
6. maintain a contemporaneous record of their work that includes their motivation and approach, results, insights and conclusions
7. write a formal report that presents the results of a scientific investigation, draws appropriate conclusions and cites the published literature to compare results and place them into the wider context of the field.

Outline Syllabus

In this module students will undertake a range of experiments, studying exciting low temperature and semiconductor physics phenomena. The experiments are designed to develop and support understanding of important effects such as superconductivity and light emission from lasers, which have great significance for current and future technologies. Tours of the related facilities in the Lancaster Quantum Technology Centre will provide an introduction to the contemporary research in these areas. A laboratory manual is provided, to prompt and support the students as they plan and complete in-depth investigations. The students will learn how to operate advanced laboratory equipment including cryogenic apparatus, allowing them to observe exotic physics such the properties of superfluid 4He. They will also gain an awareness of important semiconductors and their band structure. Possible experiments include the study of superconductivity and the characteristic phenomena of superconductivity zero resistivity and magnetic flux exclusion (Meissner effect); measurement of the bandgap energy in the common semiconductor materials; an exercise to design an experimental cryostat insert for experiments at 4K; characterisation of the spontaneous photon emission from an LED; an experimental investigation of the suitability and use of thermometers over the temperature range from room temperature to near 1K; spectroscopic analysis of the stimulated emission spectrum from a semiconductor laser; experiments on superfluid turbulence using vibrating wire resonators; measuring how the behaviour of a semiconductor device depends on its temperature and an experimental study of the novel second sound mode (temperature wave) in superfluid 4He. An introduction is given to the experiments, including how to work safely with lasers and cryogenic liquids.

Assessment Proportions

The module convenor(s) will be present during the lab sessions to oversee safety, regularly check on progress, provide feedback for formative assessment, and help with problems or questions. Practical skills are developed through guidance and demonstration from the module convenor(s). The optional weekly office hour provides an opportunity for students to speak to the module convenor(s) individually and to receive further feedback. Assessment consists of a continuous element (50%) and final report (50%). The continuous element takes the form of an electronic logbook – a contemporaneous account of the work of each student, with individual and group elements and an interim presentation. The module convenor checks the logbook periodically throughout the lab to provide formative assessment and provide written feedback. Logbooks are periodically marked for summative assessment.

In the final weeks, the students will work on their reports with guidance provided on what is expected from the report. Student will be able to discuss feedback on their earlier work on their chosen report subject and get feedback on their planned report structure. Students will be able to complete their reports outside of the lab, including conducting some review of the literature to place their results into context.

PHYS6153: Astrophysical Data Lab

• Terms Taught: Michaelmas
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Introductory level coding / data analysis, experimental physis, astrophysics

Course Description

This module will provide students with an opportunity to experience practical aspects of astrophysics, solar system physics, and cosmology, framed as a series of data analysis activities. It is designed to reinforce understanding of astronomical phenomena introduced in lectures by allowing students to deduce astrophysical laws and relationships via their own analysis of real observational and simulation data sets. This will prepare students for the subsequent level 6 Astrophysics Group Project and level 7 Year 4 Projects in Astrophysics, space science or cosmology. The module is being offered as a core component of our Physics with Astrophysics programme and is consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.

Educational Aims

Upon successful completion of this module students will be able to…

1. conduct data analysis exercises in astrophysics, space science and cosmology using data collected remotely by observatories such as telescopes or spacecraft, or from simulations
2. develop simple computer code to read, manipulate, and graphically display data and the results of data analyses, and to develop models and perform simulations
3. demonstrate how knowledge of basic astronomical phenomena can be derived through such analyses; deduce astrophysical laws or causal relationships via the analysis of experimental data
4. work effectively with colleagues to achieve a common goal, solve problems and obtain results
5. keep a contemporaneous record of their work that includes their motivation and approach, results, and conclusions
6. write a formal report that presents the results of a scientific investigation, draws appropriate conclusions and cites the published literature to validate results and place them into the wider context of the field.

Outline Syllabus

The purpose of this laboratory module is to familiarise students with modern astrophysical research practices via analysis of observational and simulation data. Observational data will be sourced from a variety of research facilities in astronomy and space science. A laboratory manual is provided to assist students in conducting the analyses, and to pose questions to prompt analytical thinking. During the lab, students are encouraged to devise and perform any additional data analysis or modelling which they think might give further insights into the physics investigated. Students will conduct a set of data analysis exercises using modern computational and programming techniques. Possible exercises include exploring the connections between galaxy colour, morphology and environment using real astronomical data; understanding how physical properties such as galaxy mass and star formation rate can be derived from observations; using the cosmic distance ladder of parallax, Cepheid variable stars and supernovae to derive a value for the Hubble constant; investigating the effect of Dark Energy on cosmological models; unveiling the presence of Dark Matter within a galaxy by studying its rotation; the construction of a Hertzsprung-Russell diagram from stellar magnitude and temperature data; analysis of stellar spectra to determine how the temperature of a star influences the strength of their different absorption lines; using observations of the Sun’s photosphere and magnetic field to deduce cycles in the level of solar activity; analysis of in-situ spacecraft data from the solar wind and interplanetary magnetic field to understand their origins, and the relationships between transient solar wind phenomena such as coronal mass ejections to the solar activity cycle; modelling the coupling mechanisms between the solar wind and magnetosphere and the resulting space weather.

Assessment Proportions

Assessment consists of a continuous element (50%) and final report (50%). The continuous element takes the form of an electronic log book – a contemporaneous account of the work of each student pair. The module convenor checks the log book periodically throughout the lab to provide formative assessment and provide written feedback. Logbooks are periodically marked for summative assessment.? In the final weeks, the students will work on their reports, beginning with some guidance from the convenors on what is expected from the report. Student will then be able to complete any unfinished elements of their chosen lab, discuss their log-book feedback on their chosen lab, and get feedback on the planned structure of their report. Students will be able to complete their reports outside of the lab, including conducting some review of the literature to place their results into context.

PHYS6169: Cosmology and Space Physics

• Terms Taught: Michaelmas
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Intermediate level university physics and maths.

PHYS6171: Field Theory in Quantum Mechanics

• Terms Taught: Michaelmas
• US Credits: 5 
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including quantum mechanics + introductory level coding

Course Description

This module aims to…

• Teach an introduction to field theoretical methods used in quantum mechanics, with appropriate mathematics, building on content from FHEQ level 5, consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.
• Provide students with the opportunity to practice relevant mathematics skills and to develop their skills in solving problems in advanced quantum mechanics.
• Provide students with the opportunity to undertake an independent open-ended investigation, in line with requirements of the Institute of Physics Degree Accreditation Framework.
• Further develop key skills in theoretical physics, and transferable and professional skills.

Educational Aims

Upon successful completion of this module students will be able to…

1. Explain how concepts of field theory may be applied to describe and understand quantum mechanics.
2. Apply field theoretical techniques and associated mathematics to solve problems in quantum mechanics.
3. Plan, execute and report the results of an independent theoretical physics-based investigation in a previously unfamiliar area, including the use of mathematics, numerical modelling, interpretation of data and presentation of results, and comparison with previous works, as appropriate. Write a technical, scientific report using appropriate software, adhering to ethical principles, transparency, and avoiding bias or plagiarism.
4. Perform independent and self-directed learning, and demonstrate analytic skills by paying attention to detail, describing advanced concepts using logical arguments and correct technical language.
5. Demonstrate an appreciation of ethical scientific behaviour and of the importance of equality, diversity and inclusion in professional activities. Recognise intellectual property, environmental, and sustainability issues in the context of theoretical physics, and evaluate the broader impact of physics, mathematics and Lancaster University locally and globally.

Outline Syllabus

The module provides an introduction to field theoretical methods in quantum mechanics, and associated mathematics. It presents algebraic methods including creation and annihilation operators for the harmonic oscillator, spin operator algebra and the addition of angular momentum. Methods to describe multi-particle systems include the density matrix and partial trace, and the module introduces the concept of entanglement. For indistinguishable particles, second quantisation and some simple applications are presented. Electronic tight-binding models and their simulation are described. The module presents complex analysis including analytic functions and Cauchy-Riemann conditions; Contour integrals, Cauchy’s theorem and Cauchy’s integral formula; Laurent series, poles, residues and the residue theorem including applications. The module provides an introduction to the path integral formulation of quantum and statistical mechanics including applications of the path integral (the semiclassical approximation and WKB approximation, decay, instantons, Berry Phase). It presents key concepts of field theory in the context of quantum mechanics including linear response, Green’s functions and their path integral formulations, Wick’s theorem and the effective action. Essential physics skills are developed including ethical behaviour, IT skills including the preparation of documents, intellectual property, environmental and sustainability issues in the context of theoretical physics, and the societal impact of physics and mathematics and of a Lancaster degree in Theoretical Physics or Theoretical Physics with Mathematics. Students will undertake an independent theoretical physics-based investigation building on the taught material.

Assessment Proportions

The learning of topics related to ethics, EDI, IP, sustainability and the relevance of theoretical physics will be supported by online material including written material and asynchronous videos. It will be assessed by an online quiz (10% weighting). Additional, non-assessed coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback.

In the latter half of the module, students undertake an independent theoretical physics-based investigation building on the taught material. Summative assessment consists of an exam (50%) and a report (40%) about the independent investigation.

PHYS6181: Foundations of Quantum Technology

• Terms Taught: Michaelmas term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and Quantum Mechanics.

Course Description

This module aims to…

• Teach common themes in quantum technology which is an advanced topic related to an area of strong research activity within the Physics Department, building on content from FHEQ levels 4 and 5.
• Provide students with the opportunity to practise relevant mathematics skills and to develop their skills in solving problems in quantum mechanics related to quantum technology.

Educational Aims

Upon successful completion of this module students will be able to…

1. Apply quantum mechanics to simple, exactly solvable problems using either matrix algebra or Dirac notation.
2. Describe concepts related to quantum dynamics, entanglement, quantum information and quantum computing.
3. Formulate problems in precise terms and identify key issues.
4. Collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

This module presents applications of quantum mechanics to common themes in quantum technology and quantum information processing. There is a revision of the axiomatic formulation of quantum mechanics and related mathematics including states and the Hilbert space; linear algebra, matrices and Dirac notation; unitary transformations quantum dynamics including the time evolution operator; observables as operators and elements of measurement theory. This is framed in the context of two-level systems (qubits) including their representation on the Bloch sphere. The module introduces entanglement in composite systems, tensor products, the density matrix, and Bell inequalities. There is a description of classical computation in terms of bits and gates, as well as the representation and manipulation of quantum information in terms of qubits and gates with circuit representations. The application to quantum communication is presented including superdense coding, quantum teleportation, and quantum key distribution. Applications to quantum computing include simple quantum algorithms, practical issues for physical implementations and error correction. Spin-based implementations are introduced based on spin precession, nuclear magnetic resonance (NMR), electron spin resonance (ESR), and Rabi oscillations. Photonic implementations are introduced based on the harmonic oscillator using operator algebra, and the concept of coherent states is introduced. Superconducting qubit systems and Rydberg atoms are described in analogy with these model systems. Physics teaching will align with the Institute of Physics Degree Accreditation Framework Principle requiring institutions to have a clear commitment to equality, diversity and inclusion in the physics curriculum. This will be enabled via resources developed within the IOP’s Inclusive Physics Curriculum project, which includes material highlighting the diversity of people who have contributed to physics and exploring some of the historical context around how physics knowledge has been constructed in the fundamental areas of physics which must be covered in an IOP accredited physics curriculum.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS6209: Atomic Physics and Problem Solving

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Intermediate university level physics and maths.

PHYS6231: Further Particle Physics

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university physics and maths + introductory particle physics

Course Description

This module aims to…

• Build on the content from FHEQ levels 4, 5 and 6, and explore more advanced topics in particle physics, consistent with the QAA Benchmark Statement for Physics, Astronomy and Astrophysics, and the Institute of Physics Degree Accreditation Framework.
• Provide students with opportunities to practice relevant mathematical techniques and to develop advanced problem solving skills particle physics.

Educational Aims

Upon successful completion of this module students will be able to…

1. Describe the successes, limitations and possible theoretical extensions of the Standard Model of particle physics.
2. Demonstrate knowledge and understanding of flavour mixing in weak interactions of hadrons and neutrino oscillations and the role of experimental data in supporting these concepts.
3. Apply knowledge and understanding of the principles of particle detection and measurement.
4. Understand limitations of current experimental techniques.
5. Formulate problems in precise terms and identify key issues.
6. Collate and process information from a variety of sources including lecture notes, textbooks and online materials.

Outline Syllabus

Expanding upon the foundations of particle physics introduced in the module pre-requisites, the phenomenology of flavour mixing in the quark sector, neutrino oscillations, heavy-quark physics and experimental methods of particle detection will be discussed. Quark structure of hadrons; addition rules of angular momenta and conservation of angular momentum in particle interactions; discrete symmetries (C, P, CP and CPT); CKM matrix and its parameterisations; unitarity constraints and the unitarity triangle; mixing of neutral heavy mesons; flavour-specific and CP-specific states; theory and observations of neutrino oscillations; CP violation; current topics of heavy flavour physics, such as c- and b-hadron production and decay analysis, top quark physics. Physics beyond the Standard Model will be discussed. Results from particle physics experiments will be used to motivate and understand these topics. Beginning with particle interactions with matter, the different detectors required to identify particles and measure their kinematics will be discussed. Design requirements for large-scale, multipurpose particle physics experiments will be presented, with a focus on current experimental activities and research within the Lancaster particle physics group, including general purpose particle detectors and experiments used to measure neutrino oscillations. Types of particle accelerator, particle beam production for experiments and beam properties (e.g. luminosity) will be discussed.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS6241: Condensed Matter Physics

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university physics and maths.

Course Description

This module will introduce foundational concepts in condensed matter physics and explore how condensed matter phenomena underpin a wide range of technologies and physics applications. Students will develop their understanding of semiconducting, magnetic and superconducting materials, and learn how these materials are used to build technologies from mobile phones to medical scanners. The module will also provide students with the opportunity to practise relevant mathematics skills and to develop their skills in solving problems in condensed matter physics.?

Educational Aims

Upon successful completion of this module students will be able to…

1. Explain how physics principles, including quantum mechanics and many-particle statistics, underpin the properties of solids.
2. Demonstrate understanding of magnetic and electronic phenomena in condensed matter systems.
3. Perform calculations of physically observable quantities relevant to condensed matter physics.
4. Formulate problems in precise terms and identify key issues.?
5. Collate and process information from different sources including lectures, lecture notes and other sources (e.g. textbooks).

Outline Syllabus

The module introduces foundational concepts in condensed matter physics, explores how material properties arise from the microscopic structure of matter, and outlines how phenomena in condensed matter physics underpin a wide range of technologies and applications. The module will review fundamental properties and microscopic structure of matter, including crystals and lattices. The concept of the reciprocal lattice will be introduced. The origins of band structure will be described and important concepts including dispersion relations, band gaps, the chemical potential, effective masses and holes will be introduced. The properties and behaviour of semiconductors will be discussed, including optical and electronic properties and the operation of basic semiconductor devices including diodes and field effect transistors. The origins of different types of magnetism will be explored, including diamagnetism, paramagnetism and ferromagnetism and antiferromagnetism. Models of the paramagnetic to ferromagnetic transition will be discussed, together with the concept of an order parameter, mean field and the Curie temperature. Important applications of magnetic materials will be described. Superconductivity will be introduced as the result of electron pairing in certain materials, and the fundamental assumptions of BCS theory will be outlined at a qualitative level. Basic properties of superconductivity will be described, together with the effect of magnetic fields on superconductors and the role of the macroscopic quantum mechanical wave function. Important technological applications of superconductivity will be discussed, including Josephson junctions, their behaviour and their uses.

Assessment Proportions

Coursework in the form of problem sets requires students to apply and consolidate their knowledge by solving previously unseen problems. Problem sets are regularly spaced across the module. The coursework is marked and returned with feedback to students within a week of submission, to ensure regular and timely signalling to them. The feedback session is used to give general feedback to the class and/or individual feedback, and to work through model solutions. The optional office hour provides another opportunity for students to speak to the module convenor individually and to receive further feedback. The coursework is given a 20% weighting of the overall module credit. The main summative assessment (80% weighting) is a time-constrained, in-person, invigilated examination to assess understanding of concepts, the ability to complete calculations and solve problems, and to think and communicate under controlled conditions.

PHYS6254: Physics Group Project

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university physics and maths + introductory level experimental physics.

Course Description

This module aims to…

• Give students experience in open-ended project work, to enhance existing problem-solving skills, and provide an opportunity to apply mathematical and data analysis techniques.
• Give students experience in team activity.
• Develop information retrieval skills, provide practice in analysis and presentation of data, and further develop skills in report writing and presentation.
• Prepare students to enable them to undertake master's level physics projects.

Educational Aims

Upon successful completion of this module students will be able to…

1. Plan, execute and report the results of an open-ended physics-based investigation that may span different or unfamiliar topics in physics.
2. Use mathematics, data analysis techniques and approximations appropriately to understand the physical world.
3. Analyse and interpret data, and present results using appropriate computer software.
4. Compare the results of experiments with expectations from model calculations and/or theoretical predictions.
5. Manage a number of different tasks successfully and establish co-operative working practices with colleagues.
6. Keep a log book or another form of contemporary record keeping to describe their individual contribution to research.
7. Retrieve and digest scientific information from a variety of sources.
8. Write a technical, scientific report using appropriate software, adhering to ethical principles, transparency, and avoiding bias or plagiarism. Demonstrate analytic skills by paying attention to detail, describing advanced concepts using logical arguments and correct technical language.
9. Give a presentation and communicate with a non-specialist audience.

Outline Syllabus

The project involves an open-ended investigation of a physics question or problem. There is no set syllabus and the question or problem - in general terms - will be defined by the lecturer. Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenon. The project will not be tightly restrained by defined limits, allowing for adaption and different solutions to a given problem. Projects vary from year to year; examples of recent projects include topics in quantum, nuclear or particle physics. Projects are likely to require and to develop computer programming skills. Students will work as part of a team (typically 4-6) and will submit a group report. In addition, there will be unassessed group presentations and an assessed individual presentation.

Assessment Proportions

Assessment consists of a group mark for the report 50% (10 credits) and individual marks for contemporary record keeping 15% (3 credits), peer assessment 20% (4 credits) and the student conference 15% (3 credits). Each group should submit a single report, and every group member will receive the same mark for the report. Reports will be marked and moderated. During the project, each individual student will complete a log book to give a contemporaneous account of their own work within the group. The module convenor signs the log book weekly and provides written feedback. At the end of the project, the log book which will be marked, giving an individual contribution to the overall mark. Peer assessment will account for relative contributions of the members of the group. To further enhance and develop communication skills, a lay summary is written and a short talk is presented at the summer student conference.

PHYS6255: Astrophysics Group Project

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university astrophysics and maths + introductory level coding / data analysis.

Course Description

This module aims to…

• Give students experience in open-ended project work, to enhance existing problem-solving skills, and provide an opportunity to apply mathematical and data analysis techniques.
• Give students experience in team activity.
• Develop information retrieval skills, provide practice in analysis and presentation of data, and further develop skills in report writing and presentation.
• Prepare students to enable them to undertake Level 7 astrophysics projects.

Educational Aims

Upon successful completion of this module students will be able to…

1. Plan, execute and report the results of an open-ended investigation that may span different or unfamiliar topics in astrophysics, cosmology or space and planetary physics.
2. Use mathematics, data analysis techniques and approximations appropriately to understand the physical world.
3. Analyse and interpret data, and present results using appropriate computer software.
4. Compare the results of experiments with expectations from model calculations and/or theoretical predictions.
5. Manage a number of different tasks successfully and establish co-operative working practices with colleagues.
6. Keep a log book or another form of contemporary record keeping to describe their individual contribution to research.
7. Retrieve and digest scientific information from a variety of sources.
8. Write a technical, scientific report using appropriate software, adhering to ethical principles, transparency, and avoiding bias or plagiarism. Demonstrate analytic skills by paying attention to detail, describing advanced concepts using logical arguments and correct technical language.
9. Give a presentation about their research and communicate with a non-specialist audience.

Outline Syllabus

The project involves an open-ended investigation of a question or problem in astrophysics, cosmology or space and planetary physics. There is no set syllabus and the question or problem - in general terms - will be defined by the module convenor(s). Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenon. The project will not be tightly restrained by defined limits, allowing for adaption and different solutions to a given problem. Projects vary from year to year and can focus on problems at all scales, from Earth’s proximity, solar system, other stars, our galaxy, other galaxies or observational cosmology. Projects can be primarily observational, numerical or theoretical/computational and are likely to require and to develop computer programming skills. Students will work as part of a team (typically 4-6) and will submit a group report. In addition, there will be unassessed group presentations and an assessed individual presentation.

Assessment Proportions

Assessment consists of a group mark for the report 50% (10 credits) and individual marks for contemporary record keeping 15% (3 credits), peer assessment 20% (4 credits) and the student conference 15% (3 credits). Each group should submit a single report, and every group member will receive the same mark for the report. During the project, each individual student will complete a log book to give a contemporaneous account of their own work within the group. The module convenor periodically reviews the log book weekly and provides feedback. At the end of the project, the log book which will be marked, giving an individual contribution to the overall mark. Peer assessment will account for relative contributions of the members of the group. To further enhance and develop communication skills, a lay summary is written and a short talk is presented at the summer student conference.

PHYS6256: Theoretical Physics Group Project

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university theoretical physics and maths + introductory level coding.

Course Description

This module aims to…

• Give students experience in open-ended project work, to enhance existing problem-solving skills, and provide an opportunity to apply mathematical and computer modelling techniques.
• Give students experience in team activity.
• Develop information retrieval skills, provide practice in analysis and presentation of data, and further develop skills in report writing and presentation.
• Prepare students to enable them to undertake master's level theoretical physics projects.

Educational Aims

Upon successful completion of this module students will be able to…

1. Plan, execute and report the results of an open-ended physics-based investigation.
2. Formulate and tackle open-ended problems including ones that may span different topics in physics (and beyond) or cover unfamiliar topics.
3. Use mathematics, computing and approximations appropriately to model the physical world.
4. Analyse and interpret data, and present results using appropriate computer software.
5. Compare the results of model calculations with previous theory and/or experiment.
6. Manage a number of different tasks successfully.
7. Establish co-operative working practices with colleagues.
8. Keep a log book or another form of contemporary record keeping to describe their independent contribution to research.
9. Retrieve and digest scientific information from various sources.
10. Write a technical, scientific report using appropriate software, adhering to ethical principles, transparency, and avoiding bias or plagiarism. Demonstrate analytic skills by paying attention to detail, describing advanced concepts using logical arguments and correct technical language.
11. Give a presentation about their research and communicate with a non-specialist audience.

Outline Syllabus

The project involves an open-ended investigation of a Theoretical Physics-based problem. There is no set syllabus and the problem - in general terms - will be defined by the lecturer. Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenon. The project will not be tightly restrained by defined limits, allowing for adaption and many different solutions to a given problem. Projects vary from year to year; examples of recent projects include using cellular automata to model dynamical systems (traffic or fluid flow, fire or disease spreading, etc.), machine learning, quantum computer simulation, chaotic dynamics. Projects are likely to require and to develop computer programming skills. Students will work as part of a team (typically 4-6) and will submit a group report. In addition, there will be two unassessed group presentations and an assessed individual presentation.

Assessment Proportions

Assessment consists of a group mark for the report 50% (10 credits) and individual marks for contemporary record keeping 15% (3 credits), peer assessment 20% (4 credits) and the student conference 15% (3 credits). Each group should submit a single report, and every group member will receive the same mark for the report. During the project, each individual student will complete a log book to give a contemporaneous account of their own work within the group. The module convenor signs the log book weekly and provides written feedback. At the end of the project, the log book will be marked, giving an individual contribution to the overall mark. Peer assessment will account for relative contributions of the members of the group. To further enhance and develop communication skills, a lay summary is written and a short talk is presented at the summer student conference.

PHYS7101: Numerical Methods and Data Analysis

• Terms Taught: Michaelmas term.
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university physics and maths + coding (e.g. Python).

PHYS7161: General Relativity

• Terms Taught: Michaelmas term.
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including relativity.

PHYS7171: Advanced Theoretical Physics

• Terms Taught: Michaelmas term.
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including quantum mechanics, creation and annihilation operators, complex analysis.

PHYS7181: Advanced Quantum Technology

• Terms Taught: Michaelmas term.
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including quantum mechanics and quantum information.

PHYS7239: Experimental Methods in Particle Physics and Gauge Theories

• Terms Taught: Lent/Summer
• US Credits: 5
• ECTS Credits: 10
• Pre-requisites: Intermediate university level physics and maths + introductory Particle Physics.

PHYS7241: Advanced Condensed Matter Physics

• Terms Taught: Lent/Summer term.
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including Condensed Matter Physics.

PHYS7262: Astrophysical Plasmas and Galaxies

• Terms Taught: Lent/Summer term
• US Credits: 5
• ECTS Credits: 10 ECTS
• Pre-requisites: Intermediate level university maths and physics including electromagnetism and astrophysics.