Theoretical Physics with an Industrial Placement Year MPhys

Core 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

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

Mathematical modelling

Mathematics is the language of science.  By framing a scientific question in mathematical language, it is possible to gain deep insight into the empirical world.  This module aims to give students an appreciation of this astonishing phenomenon.  It will introduce them to the concept of mathematical modelling via examples from throughout science, which may include biology, physics, environmental sciences, and more.  Along the way, a range of mathematical techniques will be learned that tend to appear in empirical applications.  These may include (but not necessarily be limited to) difference and differential equations, calculus, and linear algebra.

20 credits

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

Optional modules:

A student will take 20 credits from this group.

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

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

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

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

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

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

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

Optional modules:

A student will take 30 credits from this group.

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

Vector Calculus and Dynamics

Vector calculus is a fundamental tool for modelling the dynamics of all kinds of objects, both solid and fluid.  In this module, you will build on the tools of vector calculus from Mathematics Core II, combining them with tools of differential equations from the L1 Mathematical Modelling module, and applying them to understand the dynamics of physical systems.  Possible examples might include liquid, gases, plasmas, and/or planetary motion.  The tools developed here will build valuable knowledge for the study of fluid dynamics and other applied mathematics modules at higher levels.

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

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

Differential equations are perhaps the most important tool in applied mathematics. They are foundational for modelling all kinds of physical and natural phenomena, including fluids and plasmas, populations of animals or cells, cosmological objects (via relativity), subatomic particles (via quantum mechanics), epidemics, even political and social opinions have been modelled using differential equations. This module will build on the tools learned at Level 1 for analysing differential equations, extending them in a variety of ways. This may include topics such as bifurcation analysis, partial differential equations (which are particularly valuable for modelling things that vary in both space and time), and the effects of boundaries on the dynamics of differential equations. it will provide the foundation for essentially all applied maths modules taught at Levels 3 and 4.

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

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

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

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

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

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

Optional project modules:

A student will take 20 credits (one module) from this group.

Research project in Physics or Astronomy

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 or astronomy. 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

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:

A student will take 30 credits (three modules) from this group.

Topics in Mathematical Biology

This module focuses on the mathematical modelling of biological phenomena.  The emphasis will be on deterministic models based on systems of differential equations.  Examples will be drawn from a range of biological topics, which may include the spread of epidemics, predator-prey dynamics, cell biology, medicine, or any other biological phenomenon that requires a mathematical approach to understand.  Central to the module will be the dynamic consequences of feedback interactions within biological systems.  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.  If you did not take Scientific Computing at Level 2, you may still be able to enrol on this module, but you will need to obtain permission from the module leader first.

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

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

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

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

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

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

Quantum mechanics at an intermediate to advanced level, including the mathematical vector space formalism, approximate methods, angular momentum, and some contemporary topics such as entanglement, density matrices and open quantum systems. We will study topics in quantum mechanics at an intermediate to advanced level, bridging the gap between the physics core and graduate level material.   The syllabus includes a formal mathematical description in the language of vector spaces; the description of the quantum state in Schrodinger and Heisenberg pictures, and using density operators to represent mixed states; approximate methods: perturbation theory,  variational method and time-dependent perturbation theory;  the theory of angular momentum and spin; the treatment of identical particles; entanglement; open quantum systems and decoherence. The problem solving will provide a lot of practice at using vector and matrix methods and operator algebra techniques. The teaching will take the form of traditional lectures plus weekly problem classes where you will be provided with support and feedback on your attempts.

15 credits

Advanced Electrodynamics

This module gives a detailed mathematical foundation for modern electrodynamics, starting from Maxwell's equations, charge conservation and the wave equation, to gauge invariance, waveguides, cavities and antennas, and an introduction to quantum electrodynamics. After a brief recap of vector calculus, we explore the role of the scalar and vector potential, the multi-pole expansion of the field, the Poisson and Laplace equations, energy and momentum conservation of the fields, and waveguides and cavities. After a relativistic treatment of the fields we consider the quantisation of the electromagnetic field modes, the Hamiltonian for the dipole coupling between a field and a radiation emitter, and finally we explore the Aharonov-Bohm effect.

15 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:

A student will take 30 credits from this group.

History of Astronomy

Astronomy is at once the oldest of the exact sciences, having been practised by most ancient civilisations, and one of the youngest: modern astronomy, with its focus on the physics of astronomical objects, is only a century old. In this course we will study how astronomy developed from a simple awareness of the phases of the Moon and the existence of the planets to its present position as a major branch of physics. Although the heritage of modern astronomy is largely from the eastern Mediterranean and Mesopotamia, we will also look at astronomy as it was practised in other cultures, particularly India, China and Mesoamerica.

This unit aims to provide an introduction to the historical development of modern astronomy, with a focus on the nature of discovery in astronomy, the interplay between theory and observation, the role of technological advances, and the relationship between astronomy and physics. The course is divided into a series of thematic topics arranged in approximate chronological order, prefaced by a brief introduction to philosophy of science. In contrast to the BSc version, this unit also has a focus on non-Western astronomy, with students required to research and write a report on some aspect of the history of astronomy outside the Mediterranean/Mesopotamian area.

The unit is taught by a combination of lectures and written course resources for the main thread, with students expected to research their report on non-Western astronomy independently, in line with expectations for students at masters level ('holders will have the independent learning ability required for continuing professional development').

15 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 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, the parity and CP violations, experimental evidence for quarks and gluons, etc.

15 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

Optical Properties of Solids

The course covers the optical physics of solid-state materials. The optical properties of insulators, semiconductors, and metals from near-infrared to ultraviolet frequencies are considered, covering both established technologies and the latest developments in photonics. The infrared properties of materials are then discussed, and the course concludes with an introduction to nonlinear crystals. The module will be taught via lectures and problem classes. 

The course first develops the classical model of absorption and refraction based on Lorentz oscillators, and then discusses the use of quantum theory to understand the absorption and emission spectra. The optical properties in state-of-the-art materials are discussed in the context of photonics research and applications. The topics covered include:

Dispersion in optical materials, including optical fibres,

Interband absorption, 

Excitons, 

Luminescence, 

Low-dimensional materials, 

Free carrier effects, 

Phonon effects, 

Nonlinear crystals.

15 credits

An Introduction to General Relativity

A course on Einstein's theory of gravity. We start with the principle of equivalence, then move on to tensors. We motivate and then write down Einstein's equations. We use Schwarzschild black holes, Friedmann Robertson Walker cosmology and gravitational waves as examples. Einstein invented general relativity in 1915. The theory makes a link between geometry and the presence of energy and matter. This is expressed in the principle of equivalence, which we introduce and discuss. General relativity calls for a sophisticated mathematics called differential geometry, for which an important tool set is tensors and tensor components. We spend about the first half of the course learning about this, and using the formalism to write down Einstein's equations. We then study solutions that have been found to correspond to black holes without spin or charge, the Friedmann Robertson Walker cosmology thought to provide a useful description of the large-scale structure of the Universe, and gravitational waves that were first detected by the LIGO experiment in 2015. The course has no formal prerequisites, but it is very mathematical. Familiarity with special relativity will be helpful, but is not required.

15 credits

Topics in Mathematical Physics

This unit will introduce students to advanced concepts and techniques in modern mathematical physics, in preparation for research-level activities.

It is assumed that the student comes equipped with a working knowledge of analytical dynamics, and of non-relativistic quantum theory.

We will examine how key physical ideas are precisely formulated in the language of mathematics. For example, the idea that fundamental particles arise as excitations of relativistic quantum fields finds its mathematical realisation in Quantum Field Theory. In QFT, particles can be created from the vacuum, and destroyed, but certain other quantities such as charge, energy, and momentum are conserved (after averaging over quantum fluctuations).

We will examine links between conservation laws and invariants, and the underlying (discrete or continuous) symmetry groups of theories. We will also develop powerful calculation tools. For example, to find the rate of creation of new particles in a potential, one must evaluate the terms in a perturbative (Feynman-diagram) expansion.

For details of the current syllabus, please consult the module leader.

15 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. Both a business proposal and a pitch to investors are assessed. This modules give 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.

15 credits

Astrobiology

Does other life exist, what might it be like, and how could we find it? In this course we examine how planets are found, and what we know about them. We consider what we know about 'life' looking at what we know about the processes, origin, and evolution of life on Earth and how life has changed the planet. This leads us to ideas about how to look for alien life and to think about what that life might be like. We finish by discussing the possibilities of intelligent technological civilisations, and the future of the human race.

15 credits

Advanced Particle Physics

The module provides students with a comprehensive understanding of modern particle physics. Focusing on the standard model, it provides a theoretical underpinning of this model and discusses its predictions. Recent developments including the discovery of the Higgs Boson and neutrino oscillation studies are covered. A description of the experiments used to probe the standard model is provided. Finally the module looks at possible physics beyond the standard model.

15 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, dots and atomically thin two-dimensional materials). Band structure engineering, the main physical properties and a number of applications of low dimensional semiconductor structures are covered. The modules concludes with some examples of recent advances in the field, such as new epitaxial techniques and atomically thin two-dimensional materials.

15 credits

Introduction to Cosmology

The aim of this course is to provide students with an understanding of the Universe as its own entity. Students will learn how the contents of the Universe affect its dynamic evolution, and how we can use observations of Type 1a Supernovae and the Cosmic Microwave Background to constrain the properties of the Universe. Students will also learn about key epochs during the history of the Universe, from inflation through to nucleosynthesis, recombination, and reionisation, before learning how the first stars and galaxies started to form. Throughout a series of lectures, students will first learn that spacetime forms the fabric of the Universe, and how the contents of the Universe in the form of dark energy, dark and baryonic matter, and radiation dictate the dynamic evolution of the Universe. Students will next learn about modern precision cosmology, whereby cosmologists use observations of Type 1a Supernovae and the Cosmic Microwave Background to measure various cosmological parameters. This aspect of the course will form the basis of a computer programming-based assessment. Toward the end of the lecture course, students will learn about the epochs of inflation, nucleosynthesis, recombination and reionisation, before learning how today's stars and galaxies began to form. Finally, students will learn about current cosmological research via a literature review.

15 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

Advanced Topics in Waves and Fluid Dynamics B

Waves and Fluid Dynamics are cornerstones of Applied Mathematics.  Both relate to the flow of fluids, i.e., propagation of information, which include not only gas (e.g., air) and liquid (e.g., water), but also in more complex media (e.g., lubricants and blood), and other materials or even the fourth state of matter: plasma.  The scientific principles and mathematical techniques involved in studying these are of inherent interest.  Wave motions give rise to well-known class of partial differential equations, and relate to concepts such as standing, progressive, and shock (i.e., nonlinear) waves; we can study these using Fourier series, Laplace transform and the powerful method of characteristics.  Viscous fluid flow gives rise to the Navier-Stokes equations.  The first semester will cover some of these ideas, while the second will move onto more advanced topics, such as three-dimensional flows, boundary layers, vortex dynamics, or magnetohydrodynamics.

30 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 Noether's theorem relating symmetries and conservation laws. In the second semester, Einstein's 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.

30 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