Theoretical Physics with an Industrial Placement Year MPhys

Core modules:

Fundamentals of Physics

This module introduces the fundamentals of University Physics that are built on in later years of study.  This includes the development of data analysis skills, laboratory skills, scientific report writing and communication along with the ability to analyse physics problems and solve them using pen and paper, experiment and computer programming. Key concepts in electromagnetism, classical mechanics, thermal physics, waves and oscillations and quantum mechanics will be studied and used to develop problem solving.

50 credits

Further Mathematics for Physicists and Astronomers

This module provides the necessary additional mathematics for all students taking physics and/or astronomy degrees including those taking theoretical physics degrees. The following topics will be covered: introduce the students to vector calculus; elementary probability theory; ensure that the students have a thorough knowledge of how to apply mathematical tools to physical problems.

10 credits

Optional modules:

Introductory Mathematics for Physicists and Astronomers

This module provides the necessary introductory  level 1 mathematics for students taking physics and / or astronomy degrees except those taking theoretical physics degrees.

Topics will be covered in two equally weighted streams: Stream A: common functions of one variable, differentiation, series expansions,  integration and ordinary differential equations. Stream B:  basic complex numbers, vector manipulation, properties and applications of matrices.

20 credits

Mathematics Core

Mathematics Core covers topics which continue school mathematics and which are used throughout the degree programmes: calculus and linear algebra, developing the framework for higher-dimensional generalisation.  This material is central to many topics in subsequent courses.  At the same time, small-group tutorials with the Personal Tutor aim to develop core skills, such as mathematical literacy and communication, some employability skills and problem-solving skills.

40 credits

Introduction to Electric and Electronic Circuits

This module introduces the concepts and analytical tools for predicting the behaviour of combinations of passive circuit elements, resistance, capacitance and inductance driven by ideal voltage and/or current sources which may be ac or dc sources. The ideas involved are important not only from the point of view of modelling real electronic circuits but also because many complicated processes in biology, medicine and mechanical engineering are themselves modelled by electric circuits. The passive ideas are extended to active electronic components; diodes, transistors and operational amplifiers and the circuits in which these devices are used. Transformers, magnetics and dc motors are also covered.

20 credits

Physics of Living Systems 2

The aim is to introduce biomechanical descriptions of the human body. We look at its structure and its performance as a physical machine. The structural characteristics of human bones and tissue are investigated, together with the mechanical functions of the skeleton and musculature. Simple fluid dynamic characteristics of the body are introduced, including descriptions of blood-flow in the arteries and veins and air-flow in the lungs.

10 credits

Introduction to Astrophysics

One of four half-modules forming the Level-1 Astronomy course, PHY104 aims to equip students with a basic understanding of the important physical concepts and techniques involved in astronomy with an emphasis on how fundamental results can be derived from fairly simple observations. The module consists of three sections:

(i) Basic Concepts, Fluxes, Temperatures and Magnitudes;

(ii) Astronomical Spectroscopy;

(iii) Gravitational Astrophysics.

Parts (i), (ii) and (iii) each comprise some six lectures. The lectures are supported by problems classes, in which you will learn to apply lecture material to the solution of numerical problems.

10 credits

The Solar System

One of the four half-modules forming the Level 1 astronomy course, but may also be taken as a stand-alone module. PHY106 covers the elements of the Solar System: the Sun, planets, moons and minor bodies. What are their structures and compositions, and what dothey tell us about the formation and history of the Solar System?

10 credits

Our Evolving Universe

The course provides a general overview of astronomy suitable for those with no previous experience of the subject. The principal topics covered are (1) how we deduce useful physical parameters from observed quantities, (2) the structure and evolution of stars, (3) the structure of the Milky Way, and the classification, structure and evolution of galaxies in general, (4) an introduction to cosmology and (5) extrasolar plantets and an introduction to astrobiology. All topics are treated in a descriptive manner with minimal mathematics.

10 credits

Frontiers of Physics

This 10-credit module aims to introduce research-inspired material into the level 1 physics curriculum. The module includes three short courses on research-based topics taught by an academic who is actively involved in the research. The course will be regularly reviewed to ensure that the material is up to date and includes current areas of investigation. The module aims to show that cutting-edge physics research is often underpinned by basic concepts covered in A level and 1st year physics courses.

10 credits

The Physics of Sustainable Energy

The module will cover the physics of sustainable energy. It includes discussions framed by the book `Sustainable Energy without the Hot Air' by D MacKay and will cover current energy requirements and what energy could potentially be provided by the various forms of renewable energy. The course will commence with a discussion of the basic physics of energy, power and work and the conversion of energy from one form to another. We examine in detail the history of global energy useage and how we produce and use energy in the UK. We will then explore the impacts that this energy use has on the biosphere and climate and the public perception of such processes. The course will then focus on the energy contenet of objects and processes we take for granted and will then move on to means by which we can produce energy using renewable technologies, such as wind, wave, solar, biofuels etc. We will also examine nuclear (fusion and fission) energy and will discuss their principles and practical implementation. Finally, we will consider solutions to our energy needs, including transportation, energy conservation, carbon capture and geoengineering.

10 credits

Classical and Quantum Optics

This module introduces the foundations of classical optics. In the Autumn semester, starting with Fermat's Principle of Least Time, we derive Snell's law and the working of lenses in geometrical optics. We give a quantitative description of telescopes and microscopes. We explore the limits of geometrical optics and show that a wave theory of optics is needed to explain phenomena like diffraction and interference. We will briefly touch the Mach-Zehnder interferometer and the Michelson-Morley interferometer that is used in gravitational wave detection.

In the Spring semester we explore the electromagnetic nature of light, and present the polarisation (linear, circular, and elliptical). We introduce the concept of coherence, and use it to make a distinction between coherent light, such as that from a laser, and incoherent light from a light bulb or the Sun. Then we explore the properties of thermal light, including Wien's law, the Rayleigh-Jeans law, and how Planck reconciled their contradiction. Finally we discuss the implications of the constant speed of light, leading to the Lorentz transformations and the relativity of simultaneity.

10 credits

Core modules:

Special Relativity & Subatomic Physics

Special relativity is a key foundation of modern physics, particularly in the contexts of particle physics and astrophysics where E = mc2 and relativistic speeds are crucial concepts. In this module, the fundamental principles of special relativity will be explained, emphasising the energy-momentum four-vector and its applications to particle collisions and decays. Applications to nuclear physics include nuclear mass and binding energy, radioactive decay, nuclear reactions, nuclear fission and fusion. We will also cover the structure of the nucleus (liquid drop model and an introduction to the shell model).

10 credits

Classical and Quantum Physics for Theoretical Physics

This module provides the core level 2 physics content for the theoretical degrees. It integrates physics content with supporting mathematics and computational/practical work. Transferable skills are covered via different presentation modes for course work. A further item is employability. The module also contains one or more items of group work. Physics topics covered are classical physics and oscillations, thermal physics, quantum mechanics, properties of matter and electromagnetism. Mathematics topics are Fourier techniques and partial differential equations. Both mathematical topics are applied to a range of the physics covered and are integrated with aspects of the computational work. The module is assessed via four standard exams (15% each), three topical and one integrative covering all the taught material, and course work (40%). Students must develop and pass a portfolio to pass the module.

70 credits

Programming in Python

Teaching computer programming is a core aspect to our degree courses and is required by our accreditation body, the Institute of Physics. Python is a widely-available programming language that can be used to design powerful computer programmes suitable for scientific applications. In addition, Python is flexible, robust and is relatively easy to learn compared to other contemporary programming language. Python is also used widely in the computing industry and in research. The aim of this module is to teach the key elements of Python programming to enable students to design programs to perform tasks ranging from computational and numerical physics to data analysis and visualisation.

10 credits

Optional modules – two or three from:

Mathematics Core II

Building on Level 1 Mathematics Core, Mathematics Core II will focus on foundational skills and knowledge for both higher mathematics and your future life as a highly skilled, analytically-astute worker.  Mathematical content will focus on topics that are vital for all areas of the mathematical sciences (pure, applied, statistics), such as vector calculus and linear algebra.  This will help develop your analytic and problem solving skills.  Alongside this, you will continue to develop employability skills, building on Level 1 Core.  Finally, there will be opportunities to learn and reflect on social, ethical, and historical aspects of mathematics, which will enrich your understanding of the importance of mathematics in the modern world.

30 credits

Aspects of Medical Imaging and Technology

This module provides an introduction to medical technology, with a particular bias towards ionising and non-ionising electromagnetic radiation and its diagnostic role in medicine. The module begins with the generation and behaviour of electromagnetic waves and the breadth of technological application across the electomagnetic spectrum. This extends from magnetic resonance imaging at low energies to high energy photons in X-ray systems. The importance of radiation in diagnosis is acknowledged by discussion of imaging theory and primary imaging modalities, such as planar radiography and CT. The therapeutic role is examined by a brief consideration of radiotherapy.

10 credits

Stellar Structure and Evolution

The module aims to provide an understanding of the physical processes occurring in stars and responsible for their internal structure and evolution from the main sequence to white dwarfs, neutron stars stars and black holes. It builds on Introduction to Astrophysics (PHY104) and seeks to explain the evolutionary phenomena described in Our Evolving Universe (PHY111).

10 credits

Physics of Materials

This module provides an introduction to the physical properties of materials. Subjects covered include properties of liquids (surface tension, viscosity etc), solids (elastic properties, mechanical properties etc) and soft condensed matter.

10 credits

Detection of Fundamental Particles

The Standard Model of particle physics is one of the great success stories of late 20th century physics - but how do we obtain the data needed to construct and test this model? In this module, we will explore how typical experiments in different branches of particle physics are designed to extract the maximum possible amount of data from the interactions that they observe. This will be supplemented by laboratory and computational exercises in which students try out some of these techniques themselves.

10 credits

Galaxies

This Level 2 Astronomy half-module aims to provide a comprehensive introduction to galaxies. It consists of six parts: (i) astronomical distance determination and galaxy classification; (ii) the properties of the main stellar and a gas components of our Milky Way galaxy, and its local environment; (iii) the properties of spiral galaxies; (iv) the properties of elliptical galaxies; (v) active galaxies; (vi) galaxy evolution. Students' presentation and research skills are developed through a 2500 word essay assignment.

10 credits

The Physics of Music

This module will provide an introduction to the physics of music building on physics covered in year 1 and semester 2 of year 2. The module will include the following topics: Recap of oscillations, waves and resonance, the human voice, physics of tuned and untuned percussion, musical pitch and timbre, Fourier analysis, musical scales, physics of stringed instruments, physics of wind instruments, electric instruments (based on electro-magnetic pickups and piezoelectric transducers), synthesizers (analogue and digital), sound recording and reproduction (analogue and digital), myths, legends, folklore and pseudoscience in acoustics.

10 credits

Astronomical Spectroscopy

This level 2 module provides an overview of astronomical spectroscopy for astrophysics dual students, covering how spectrographs work, the nature of spectra, atomic physics relevant to astronomical spectroscopy, line broadening mechanisms (natural, pressure, thermal) and the Curve of Growth for the determination of ionic abundances in stellar atmospheres, plus spectral diagnostics of ionized nebulae. Content from lectures are reinforced through an exercise involving specialist astronomical software relating to nebular diagnostics, plus the manipulation of stellar spectroscopic datasets using the programming language Python for the calculation of ionic abundances.

10 credits

Differential Equations

The module aims at developing a core set of advanced mathematical techniques essential to the study of applied mathematics. Topics include the qualitative analysis of ordinary differential equations, solutions of second order linear ordinary differential equations with variable coefficients, first order and second order partial differential equations, the method of characteristics and the method of separation of variables.

20 credits

Core modules:

Particle Physics

This Level 3 Physics half module introduces students to the exciting field of modern particle physics. It provides the mathematical tools of relativistic kinematics, enabling them to study interactions and decays and evaluate scattering form factors. Particles are classified as fermions - the constituents of matter (quarks and leptons) - or as bosons, the propagators of field. The four fundamental interactions are outlined. Three are studied in detail: Feynman diagrams are introduced to describe higher order quantum electrodynamics; weak interactions are discussed from beta decay to high energy electroweak unification; strong interactions, binding quarks into hadrons, are presented with the experimental evidence for colour. The role symmetry plays in the allowed particles and their interactions is emphasised.

10 credits

Mathematical Physics

Linear algebra: matrices and vectors; eigenvalue problems; matrix diagonalisation; vector spaces; transformation of basis; rotation matrices; tensors; Lie groups; Noether's theorem. Complex analysis: analytic functions; contour integration; Cauchy theorem; Taylor and Laurent series; residue theorem; application to evaluating integrals; Kronig-Kramers relations; conformal mapping; application to solving Laplace's equation.

10 credits

Advanced Programming in Python

Python is a widely-available programming language that can be used to design powerful computer programmes suitable for scientific applications. Python is also used widely in the computing industry and in research. This module builds on the basic introduction provided in PHY235/PHY241 by introducing advanced concepts such as defensive programming, classes, program design and optimisation. This teaching will be underpinned with a series of projects which will furnish the students with the ability to design complex Python scripts to address a wide variety of problems including those involving analysis of 'big data with emphasis on presentation of results using advanced visualisation methods.

10 credits

Atomic and Laser Physics

This module covers the physics of atoms and lasers at an intermediate level. The course begins with the solution of the Schrodinger equation for the hydrogen atom and the atomic wave functions that emerge from it. It then covers atomic selection rules, spectral fine structure and the effects of external fields. The spectra of selected multi-electron atoms are described. The basic operation of the laser is then covered by introducing the concepts of stimulated emission and population inversion. The course concludes with a description of common lasers and their applications.

10 credits

Statistical Physics

Statistical Physics is the derivation of the thermal properties of matter using the under-lying microscopic Hamiltonians. The aims of this course are to introduce the techniques of Statistical Mechanics, and to use them to describe a wide variety of phenomena from physics, chemistry and astronomy.

10 credits

Solid State Physics

Covering the electronic properties of solids, this module details the classification of solids into conductors, semiconductors and insulators, the free electron model, the origin of electronic band structure, the fundamental electronic properties of conductors and semiconductors, carrier statistics, experimental techniques used to study carriers in a solid, and the classification and physics of the principal types of magnetism.

10 credits

Problem Solving in Physics

This module is a 'big picture' look at physics problem solving.  The module develops techniques for solving unfamiliar problems in physics using mathematical and statistical methods.

This module is split into two halves: Statistics and data analysis (S1), and Physics Problem Solving (S2).  

Statistics covers the basics of Frequentist vs. Baysian approaches and data analysis, and applies them to data analysis tasks from a wide range of physics. It also looks at common statistical mistakes and fallacies and examines how to present data graphically and in writing.



Physics Problem Solving uses weekly problems classes to examine how physics knowledge can be applied to unfamiliar (often 'real world') problems to obtain quick, rough, but sound and useful conclusions/answers (often known as the 'back of the envelope' approach to problem solving). Problems cover the full range of core physics, requiring identification of which aspect of physics is relevant to a particular problem.

10 credits

Project modules – one from:

Research project in Physics

The aim of this 20 credit module is to provide an opportunity for students to exercise and develop their skills and ability to undertake independent, albeit closely supervised, research in physics. A very wide selection of projects is provided, often arising from current research in the Department. Many are practical, others are essentially theoretical or interpretative or require the development of and running of computer programmes designed to simulate a variety of physical phenomena. Most projects are collaborative and encourage students to work in pairs. Assessment is based on individual written reports and oral examinations. These provide exercise in presentational skills.

20 credits

Industrial Group Project in Physics

PHY346 provides students with an industrial project where team working, planning, time management; presentation and report writing are integrated with science problem solving. The industrial client poses a problem that a group work on over two semesters to resolve. Interim and final presentations are made to the client and academic supervisors. Project work may use laboratory measurement and computational approaches as well as referencing leading research literature.

20 credits

Quantum Information Laboratory

This predominantly laboratory-based module provides a foundation in quantum optics experiments and associated theory. The quantum nature of light will be studied in core experiments involving single photon generation and detection, measurements of photon statistics and photon interference. Experimental activities will be supported by a series of lectures and problems classes. The link with quantum information research is made through research seminars from university research groups and companies, plus a 'journal club' where key scientific papers are presented and discussed. Transferable skills acquired will prepare students for higher study and employment in industries involving quantum technologies.

20 credits

Microscopy and Spectroscopy Laboratory

This module will develop transferrable skills that will be useful in further experimental project work and industrial science and technology roles. Students will gain hands-on experience using a range of sophisticated experimental techniques to explore physics research and real world context-based questions. Atomic force microscopy (AFM), optical and gamma-ray spectroscopies, as well as associated techniques such as ellipsometry will be used. Students will undertake a series of experiments, supported by lectures, in semester one and conduct an open-ended project utilising the techniques in semester two.

20 credits

Physics Education and Outreach

This 20-credit Extended Project unit is intended primarily for students considering a career in teaching, but may also be of interest to those wishing to pursue careers in science communication in general. The first half of the unit will introduce a range of topics including theory of learning and teaching, skills such as video editing, physics in the National Curriculum, and a range of hands-on exercises in science teaching and communication. Students will undertake a range of assignments related to the taught material, which may include lesson observations in schools, making videos or podcasts, radio broadcasts, writing popular articles or creating resources for schools. The second half consists of a 10-credit project: a wide range of schools and outreach-related topics are available.

Note that admission to this unit is subject to an interview and a DBS check. This is because parts of the unit require students to visit schools and interact with pupils.

20 credits

Optional modules – three from:

Continuum Mechanics

Continuum mechanics is concerned with the mechanical behaviour of solids and fluids which change their shape when forces are applied. For example, rubber extends when pulled but behaves elastically returning to its original shape when the forces are removed. Water starts to move when the external pressure is applied. This module aims to introduce the basic kinematic and mechanical ideas needed to model deformable materials and fluids mathematically. They are needed to develop theories which describe elastic solids and fluids like water. In this course, a theory for solids which behave elastically under small deformations is developed. This theory is also used in seismology to discuss wave propagation in the Earth. An introduction in theory of ideal and viscous, incompressible and compressible fluids is given. The theory is used to solve simple problems. In particular, the propagation of sound waves in the air is studied.

10 credits

Mathematical modelling of natural systems

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

10 credits

Fluid Mechanics I

The way in which fluids move is of immense practical importance; the most obvious examples of this are air and water, but there are many others such as lubricants in engines. Moreover, the scientific principles and mathematical techniques needed to explain fluid motion are of intrinsic interest. This module builds on Level 2 work (MAS222 Differential Equations; MAS280 Mechanics and Fluids). The first step is to derive the equation (Navier-Stokes) governing the motions of most common fluids. This serves as a basis for the remainder of MAS320, with the main addition to MAS280 being that it covers viscous (frictional) fluids.

10 credits

Differential Geometry

What is differential geometry? In short, it is the study of geometric objects using calculus. In this introductory course, the geometric objects of our concern are curves and surfaces. Besides calculating such familiar quantities as lengths, angles and areas, much of our focus is on how to measure the 'curvature' of a geometric object. The story is relatively simple for curves, but naturally becomes more involved for surfaces - and more interesting too.

10 credits

Mathematical Biology

This module provides an introduction to the mathematical modelling of the dynamics of biological populations. The emphasis will be on deterministic models based on systems of differential equations that encode population birth and death rates. Examples will be drawn from a range of different dynamic biological populations, from the species level down to the dynamics of molecular populations within cells. Central to the module will be the dynamic consequences of feedback interactions within the populations. In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used.

10 credits

Nuclear Physics

This half-module Level 3 Physics course aims to study the general properties of nuclei, to examine the characteristics of the nuclear force, to introduce the principal models of the nucleus, to discuss radioactivity, to study nuclear reactions, in particular fission and fusion, and to develop problem solving skills in all these areas. The motivation is that nuclear processes play a fundamental role in the physical world, in the origin of the universe, in the creation of the chemical elements, as the energy source of the stars and in the basic constituents of matter - plus the best of all motives - curiosity.

10 credits

Introduction to Cosmology

Cosmology is the science of the whole Universe: its past history, present structure and future evolution. In this module we discuss how our understanding of cosmology has developed over time, and study the observed properties of the universe, particularly the rate of expansion, the chemical composition, and the nature of the cosmic microwave background, can be used to constrain theoretical models and obtain value for the parameters of the now-standard Hot Big Bang cosmological model.

10 credits

Physical Computing

Digital circuits underpin our modern lives, including the acquisition and processing of data for science. In this course we will study the fundamental building blocks of digital processing circuits and computers. We will learn to describe circuits using the language VHDL, and how to program computers using the hardware-oriented high level language C. We will build interesting and useful digital architectures, and apply the skills we have acquired in laboratory exercises.

10 credits

Astrobiology

Is anybody out there? In this module we explore how we hope to find alien life in the near future and discuss what this might be like and where we should be looking. We critically examine ideas about the frequency of life, advanced life, and technological civilisations in the universe.

10 credits

Physics in an Enterprise Culture

This is a seminar and workshop based course where students will create a proposal for a new business. Seminars will cover topics such as innovation, intellectual property, costing and business planning. Workshops will support students to develop ideas and communicate them effectively. This module gives students an opportunity to develop a business proposal, using their physics knowledge as a starting point.  The module starts with a series of seminars and workshops designed to help students come up with possible new ideas for products or services that they are interested in developing further. Further seminars formalise how business ideas are tested to ensure that basic assumptions about customers and markets are sensible and also guidance is given in terms of how to estimate the costs and revenues associated with the idea. Finally seminars to support writing the idea into a proposal are given. Evaluation of ideas using peer feedback is a key part of the module and midway through a review panel is organised to give an opportunity for students to formally evaluate other ideas to help them develop their own.

10 credits

Dark Matter and the Universe

This course aims to provide students with an understanding of Dark Matter in the Universe from both the astrophysics and particle physics viewpoints. This course is split into two halves. The first half of the course is on the astrophysical evidence for Dark Matter, and the second half of the course is on the detection of candidate Dark Matter particles. The main teaching method is the standard 50-minute lecture, which is well suited to the delivery of the factual information in this course. This is backed up by a blackboard site containing copies of the lecture notes, lecture recordings, and non-assessed exercises.



The syllabus will include the astrophysical evidence for dark matter in the Universe, the search for dark matter candidates, including direct and indirect searches for Weakly Interacting Massive Particles (WIMPs), the search for supersymmetry at the Large Hadron Collider, and axion searches.

10 credits

Semiconductor Physics and Technology

This module builds on the core solid state physics modules to provide an introduction to semiconductor electronic and opto-electronic devices and modern developments in crystal growth to produce low dimensional semiconductor structures (quantum wells, wires and dots). Band structure engineering, the main physical properties and a number of applications of low dimensional semiconductor structures are covered.

10 credits

Introduction to Soft Matter and Biological Physics

Soft matter includes materials with properties between those of solids and liquids, for example plastics, gels, soaps, foods, biological cells and tissues. The behaviour of these complex materials depends on elegant physical principles determining the interactions within and between molecules. Using these physical principles we will explore molecules essential to life, such as proteins and DNA, and materials key to technology, such as polymers.We will start by defining what is soft matter by considering states of matter and the relevant length, time and energy scales. Next we will describe the important intramolecular and intermolecular interactions. Statistical mechanics models will enable us to predict bulk properties from molecular parameters. We will introduce experimental measurements and imaging techniques that are used to investigate soft matter and biological systems. We will introduce polymers and key properties of polymers such as viscoelasticity. We will introduce essential biopolymers including DNA and proteins. 

We will provide an introduction to systems of interest, for example polymer materials, colloids, liquid crystals or membranes and discuss their properties and assembly.

10 credits

Origin of the Chemical Elements

This course looks at the origin, distribution and evolution of the chemical elements, which are created in the early Universe, during the life cycles of stars and in the interstellar medium.The main teaching method is the standard 50-minute lecture, which is well suited to the delivery of the factual information in this course. This is backed up by a blackboard site containing copies of the lecture notes, lecture recordings, and non-assessed exercises. Syllabus includes topics such as: Experimental evidence for elemental abundances; Observational evidence for elemental abundances; Primordial nucleosynthesis; Stellar nucleosynthesis; Neutron capture Supernovae and kilonovae; Cosmic rays.

10 credits

Core modules:

Advanced Quantum Mechanics

This module presents modern quantum mechanics with applications in quantum information and particle physics. After introducing the basic postulates, the theory of mixed states is developed, and we discuss composite systems and entanglement. Quantum teleportation is used as an example to illustrate these concepts. Next, we develop the theory of angular momentum, examples of which include spin and isospin, and the method for calculating Clebsch-Gordan coefficients is presented. Next, we discuss the relativistic extension of quantum mechanics. The Klein-Gordon and Dirac equations are derived and solved, and we give the equation of motion of a relativistic electron in a classical electromagnetic field. Finally, we explore some topics in quantum field theory, such as the Lagrangian formalism, scattering and Feynman diagrams, and modern gauge field theory.

10 credits

Research project

Students will undertake a supervised research project during the whole of the 4th year of an MPhys degree, applying their scientific knowledge to a range of research problems experimental and/or theoretical projects spanning the research expertise of the Department. Along with applying their knowledge, students will manage their project, ensuring that they develop skills in time management, project planning, scientific record keeping, information retrieval and analysis from scientific and other technical information sources.

60 credits

Optional modules – three or four from:

Topics in Advanced Fluid Mechanics

This module aims to describe advanced mathematical handling of fluid equations in an easily accessible fashion. A number of topics are treated in connection with the mathematical modelling of formation of the (near-)singular structures with concentrated vorticity in inviscid flows. After discussing prototype problems in one and two dimensions, the three-dimensional flows in terms of vortex dynamics are described. Key mathematical tools, for example, singular integrals and calculus inequalities, are explained during the unit in a self-contained manner. Candidates are directed to read key original papers on some topics to deepen their understanding.

20 credits

Analytical Dynamics and Classical Field Theory

Newton formulated his famous laws of mechanics in the late 17th century. Later, mathematicians like Lagrange, Hamilton and Jacobi discovered that underlying Newton's work are wonderful mathematical structures. In the first semester we discuss this work, its influence on the subsequent formulation of field theory, and Noethers theorem relating symmetries and conservation laws.
In the second semester, Einsteins theory of gravity, General Relativity, will be introduced, preceded by mathematical tools such as covariant derivatives and curvature tensors. Einstein's field equations, and two famous solutions, will be derived. Two classic experimental tests of General Relativity will be discussed.

20 credits

Mathematical modelling of natural systems (Advanced)

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

10 credits

Magnetohydrodynamics

Magnetohydrodynamics has been successfully applied to a number of astrophysical problems (eg to problems in Solar Magnetospheric Physics), as well as to problems related to laboratory physics, especially to fusion devices. This module gives an introduction to classical magnetohydrodynamics. Students will get familar with the system of magnetohydrodynamic equations and main theorems that follow from this system (e.g. conservation laws, anti-dynamo theorem). They will study the simplest magnetic equilibrium configurations, propagation of linear waves, and magnetohydrodynamic stability. The final part of the module provides an introduction to the theory of magnetic dynamo

10 credits

Physics in an Enterprise Culture

This is a seminar and workshop based course with a high level of student centred learning. The unit will introduce students to the methods and skills associated with innovation, business planning, costing and marketing. It will broaden students understanding of the mechanics of project planning and research commercialisation. The course is divided into two components:

Part 1: Coming up with ideas. Students will take part in guest lectures and workshop classes to explore different ideas for business. They will learn about the innovation process and what makes a sucessful business. They will finish part 1 by submitting a draft business proposal that will be reviewed by academic staff and student peers and feedback will be given.

Part 2: Armed with the feedback from part 1 students will refine thier ideas and work towards a final pitch for thier business. Further support will be given to students to develop a costing of the idea.

10 credits

History of Astronomy

The module aims to provide an introduction to the historical development of modern astronomy. After a brief chronological overview and a discussion of the scientific status of astronomy and the philosophy of science in general, the course is divided into a series of thematic topics addressed in roughly chronological order. We will focus on the nature of discovery in astronomy, in particular the interplay between theory and observation, the role of technological advances, and the relationship between astronomy and physics.

10 credits

Advanced Particle Physics

The main aim of the unit is to give a formal overview of modern particle physics. The mathematical foundations of Quantum Field Theory and of the Standard Model will be introduced. The theoretical formulation will be complemented by examples of experimental results from the Large Hadron Collider and Neutrino experiments. The unit aims to introduce students to the following topics:
- A brief introduction to particle physics and a review of special relativity and quantum mechanics
- The Dirac Equation
- Quantum electrodynamics and quantum chromo-dynamics
- The Standard Model
- The Higgs boson
- Neutrino oscillations 
- Beyond the Standard Model physics

10 credits

Semiconductor Physics and Technology

This module builds on the core solid state physics modules to provide an introduction to semiconductor electronic and opto-electronic devices and modern developments in crystal growth to produce low dimensional semiconductor structures (quantum wells, wires and dots). Band structure engineering, the main physical properties and a number of applications of low dimensional semiconductor structures are covered.

10 credits

The Development of Particle Physics

The module describes the development of several crucial concepts in particle physics, emphasising the role and significance of experiments. Students are encouraged to work from the original literature (the recommended text includes reprints of key papers). The module focuses not only on the particle physics issues involved, but also on research methodology - the design of experiments, the critical interpretation of data, the role of theory, etc. Topics covered include the discoveries of the neutron, the positron and the neutrino, experimental evidence for quarks and gluons, the neutral kaon system, CP violation etc.

10 credits

Advanced Soft Matter and Biological Physics

Fascinating behaviour of soft matter and biological systems often occurs at thermal energy scales and can be described by statistical mechanical models. In addition, living biological matter is driven out of equilibrium due to internal biochemical sources of energy. Mathematical models and modern advanced experimental techniques are revealing the physical principles underpinning the biological world and the technological possibilities of complex soft materials.Much recent progress in soft matter and biology has been made thanks to the advent of advanced experimental  techniques which we will show are based on elegant physical principles. We will also study the physical principles underpinning the behaviour of complex soft matter and biological materials. We will describe phase transitions in multiple soft matter systems by calculating free energies. We will use random walk models to describe the shape of polymer molecules and the Brownian motion of colloids. We will also study the dynamics of polymers and the kinetics of polymerisation. We will then consider how polymerisation of protein filaments and action of molecular motors can generate forces in biological cells. This will involve us introducing concepts of systems that are in equilibrium versus out of equilibrium. Using a mathematical  framework we can describe behaviour at different length scales for example from the cytoskeleton to tissues, bacteria colonies and flocking. We will also investigate how the energy required for life is captured in photosynthesis.

15 credits

Directed reading in Physics and Astrophysics

This short module gives Masters students the opportunity to explore in detail a topic of interest to them, making use of research literature and/or graduate texts as appropriate.  Students will select the topic (subject to approval by the module leader) and be assigned a supervisor with appropriate expertise.  (Note: suggested topics may have to be rejected if no suitably qualified supervisor is available.)  Students will develop their understanding of the chosen topic by reading appropriate literature, as identified by the student with guidance from the supervisor.  If appropriate to the topic, students may also undertake other activities, particularly coding. 

   The module aims to encourage students to learn independently using research-level sources.  Consequently, there is no formal teaching.  Students are guided by weekly supervision sessions in which supervisors will discuss that week’s reading with the student, provide feedback and suggestions for further reading, help with any points that the student has found difficult to understand, and correct any misconceptions.  Students will keep a study diary in which they keep notes of their sources, explain topics in their own words, and perhaps work through problems.  In some cases, other activities, especially coding, may be undertaken to explore aspects of the topic. 

5 credits

Optical Properties of Solids

This course covers the optical physics of solid state materials. It begins with the classical description of optical propagation. It then covers the treatment of absorption and luminescence by quantum theory, and the modifications caused by excitonic effects. The phenomena are illustrated by discussing the optical properties of insulators, semiconductors, and metals. The infrared properties of ionic systems are then discussed, and the course concludes with a brief introduction to nonlinear crystals.

10 credits

An Introduction to General Relativity

This module introduces coordinate systems and transformations in Euclidean space. The principles of special relativity are reviewed, with emphasis on the coordinate transformations between systems moving at constant velocities. Our discussion of general relativity begins with an introduction to the principle of equivalence. We introduce the Christoffel symbols and the curvature tensors. We study examples of phenomena affected by general relativity, the rate of clocks and the redshift and bending of light in a gravitational field. Finally, we examine space time in the vicinity of the event horizon, the geometry of a non-spinning black hole, and the geometry of wormholes.

10 credits

Introduction to Cosmology

The module will cover advanced astrophysics topics involving observations and theory of star and planet formation, plus the evolution of low, intermediate and high mass single stars, close binary evolution including their end states (white dwarfs, neutron stars, black holes), supernovae and gamma ray bursts.

10 credits

Quantum Optics and Quantum Computing

Quantum computing is introduced through the fundamental concepts of quantum gates and circuits before moving to cover more advanced topics such as quantum programming, quantum algorithms and quantum error correction. These concepts are then applied by studying how programming quantum circuits can be done using cloud computers (e.g. using openQASM format) and the implementation of quantum algorithms (including examples) and quantum error correction using stabiliser formalism and graph states and quantum error correction codes.

The second part of the module covers quantum optics and quantum optical applications at the forefront of current research in the field. This includes topics such as weak and strong coupling of dipole sources in a cavity, single photon sources, protocols of quantum optical communications and linear optics computation. The module then progresses to quantum optical applications. Cavity electrodynamics is studied in the regimes of strong and weak coupling of matter excitations to the electromagnetic field in optical microstructures. This will lead to the physics of highly efficient single photon devices necessary for linear optics quantum computation. The effects of entanglement and quantum teleportation will be also considered.

15 credits