
SEM1
4
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: Practical work in the laboratory serves to illustrate basic concepts in physics, and the processes of carrying out experiments and interpreting their
results. You will be taught techniques of measurement and the use of instruments and computers. There are some lectures on statistics and data analysis, which
are applied to the laboratory measurements. There is no final examination. All assessment is by coursework and laboratory reports.
Assessment: 100.0% Coursework
Level: 4

Mathematical Techniques I
SEM1
4
15
Overlap: None
Prerequisite: None
Corequisite: None
Prerequisite of: SPA4XXX;SPA5241; SPA5666; SPA6309
Description: Techniques of mathematics, mostly calculus, required in the study of the physical sciences. Topics will include vectors and scalars,
vector components, addition and multiplication, complex numbers and functions, differentiation, partial differentiation, series, integration, polar coordinates and multiple integration. The course structure includes both lectures and selfpaced programmed learning, with assessment by coursework and an end of year examination.
Assessment: 80.0% Examination and 20.0% Coursework
Level: 4

Classical Physics
SEM1
4
15
Overlap: None
Prerequisite: None
Corequisite: None
Prerequisite of: SPA5241; SPA5666; SPA6309
Description: This module reviews the classical understanding of space, time and motion: the fundamental physical principles that underpin modern physics.
We begin with an overview of classical mechanics, where we will study kinematics and dynamics; rotational motion; dynamics of a rigid body and the gyroscope; and gravity and planetary orbits. In the second part of the module, we focus on oscillatory phenomena and wave motion, which occur throughout nature in fields from biology to quantum mechanics. Topics will include the 1D wave equation; free, damped, forced and coupled oscillations; resonance and driven simple harmonic motion; calculations of normal modes for coupled oscillators; waves in linear media including gases and solids; dispersion, phase and group velocity; interference, beats and standing waves; simple diffraction phenomena; and the Doppler effect in sound and light.An introduction to the basic laws of electromagnetism: electric force and field; electric potential and energy; capacitance; electromotive force; introduction to electromagnetic waves; applications in science and engineering.
Assessment: 80% Examination and 20% Coursework
Level: 4

Modern Physics
SEM1
4
15
Overlap :None
Prerequisite: None
Corequisite: None
Prerequisite of: SPA5241; SPA5666; SPA6309
Description: This module covers the dramatic developments in physics that occurred in the early twentieth century, introducing special and general relativity and quantum theory. In relativistic mechanics we will study special relativity; the Lorentz transformation; length contraction and time dilation; the clock paradox; relativistic kinematics and dynamics; general relativity and its tests and consequences; and black holes and galactic lenses. In quantum theory, we will study descriptions of the evidence for particlelike properties of waves, and wavelike properties of particles, followed by their consequences and their formal expression in physical law: topics include Heisenberg's uncertainty principle, Schrodinger's equation and elementary quantum mechanics. We will also introduce the fundamental particles and the forces of the standard model of particle physics.
Assessment: 80% Examination and 20% Coursework Level: 4

Mathematical Techniques 3
SEM1
5
15
Overlap: None
Prerequisite: SPA4122 or equivalent
Corequisite: None
Prerequisite of: SPA5304, SPA6324; SPA6325; SPA6413; SPA7018U/P
Description: In this module some advanced mathematical techniques are developed in the context of solving real physical problems. Computer algebra (MAPLE) is used in the practical classes to enable you to learn a professional physicists approach to real problemsolving.
Assessment: 80% Examination and 20% Coursework Level: 5

Thermodynamics
SEM1
5
15
Overlap: None
Prerequisite: SPA4121 or equivalent courses of elementary calculus and mechanics
Corequisite: None
Description: Thermal and Kinetic Physics is a course designed as an introduction to the notion of energy and its transformations. The thermodynamic methodology that is constructed, largely through the paradigm of the ideal gas, is widely applicable throughout the realm of physics. We begin by developing a language capable of dealing with the thermodynamic method and this requires that concepts of equilibrium and temperature are disentangled before work and heat are described in detail en route to the First Law of Thermodynamics. With the First Law many things become readily accessible to an analytic approach previously unavailable including; engines, refrigerators and heat pumps. Entropy will then make a natural appearance as a macroscopic thermodynamic variable in the build up to the Second Law of Thermodynamics with a brief look at its microscopic origins. New thermodynamic potentials including the Gibbs potential and the Helmholtz free energy, and their applications, are discussed in order to generalise further the thermodynamic method. Phase changes for simple systems are briefly covered and the Third law of Thermodynamics described. Finally an introduction to the kinetic description of gases in equilibrium and of phenomena such as diffusion and heat conduction will complete the module.
Assessment: 80% Examination and 20% Coursework Level: 5

Nuclear Physics and Astrophysics
SEM1
5
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: A module describing subatomic phenomena and explaining them in terms of the theories of quantum physics and relativity: nuclear properties, reactions and decays; Nuclear astrophysics and its cosmological consequences.
Assessment: 70% Examination and 30% Coursework Level: 5

Quantum Mechanics A
SEM1
5
15
Overlap: None
Prerequisite:
Corequisite: None
Prerequisite of: SPA6306; SPA7029U/P
Description: This course aims to introduce the fundamental concepts of quantum mechanics from the beginning. By studying applications of the principles of quantum mechanics to simple systems the course will provide a foundation for understanding concepts such as energy quantisation, the uncertainty principle and quantum tunnelling, illustrating these with experimental demonstrations and other phenomena found in nature. These concepts are introduced and applied to systems of increasing (mathematical) complexity: (i)Infinite 1D quantum wells. (ii)Finite 1D quantum wells (introducing graphical solutions of transcendental equations). (iii)LCAO methods for modelling ions. (iv)Simple Harmonic oscillators (introducing Hermite polynomials and applying energy solutions to molecular vibrational spectra). (v)Beams of free particles, probability flux and reflection/transmission in stepwise varying potentials. (vi)Finite potential barriers and tunnelling, Tunnelling through arbitrary potential barriers (the Gamow factor), field emission and Alpha decay and tunnelling. The Scanning Tunnelling Microscope (STM). (vii)The solution to the Hydrogen atom, including separation of variables, spherical harmonics, the radial equation and electronic energy levels and the quantum numbers n, l, ml and ms and resulting degeneracy. (viii)The treatment of angular momentum in quantum mechanics, its magnitude and projection along an axis. (ix)Introduction to first order, time independent, perturbation theory.
Assessment: 80% Examination and 20% Coursework Level: 5

Stars
SEM1
5
15
Overlap :None
Prerequisite: None
Corequisite: None
Description: Stars are a vital building block in the Universe: forming out of interstellar gas and dust, and themselves being a major component of galaxies. They are also vital for providing the nuclear reactions that create the elements from which planets and even ourselves are formed. This course describes how the fundamental properties of stars are related to observations. Temperatures and densities in the centre of stars reach values that are unattainable in the laboratory. Yet the application of basic physical principles can help us determine much about the internal structure and evolution of stars, from their formation to their ultimate end states in such exotic and spectacular objects as white dwarfs, neutron stars and black holes.
Assessment: 80% Final Examination, 10% MidTerm Test and 10% Coursework Level: 5

Elementary Particle Physics
SEM1
6
15
Overlap: None
Prerequisite: SPA5319 or equivalent introductory course in quantum physics
Corequisite: None
Description: An introduction to the standard model of particle physics  the strong and electroweak interactions between the basic constituents of the world, quarks and leptons, via the exchange of gluons, photons and W and Z particles. Recent results on CP violation and neutrino mixing. The search for the Higgs particle. Beyond the standard model  Grand unified theories and supersymmetry.
Assessment: 80% Examination and 20% Coursework Level: 6

Spacetime and Gravity
SEM1
6
15
Overlap: None
Prerequisite: None
Corequisite: None
Prerequisite of: SPA7027U
Description: This course presents the essential concepts of both special and general relativity. The emphasis is on the physical understanding of the theory and the mathematical development is kept simple, although more detailed treatments are included for those who wish to follow them; spacetime diagrams being are used extensively. The course includes discussion of the big bang and black holes.
Assessment: 85% Examination and 15% Coursework Level: 6

Physical Cosmology
SEM1
6
15
Overlap: SPA7005
Prerequisite: Ideally SPA6308
Corequisite: None
Prerequisite of: SPA7028U
Description: his module covers the essential concepts of modern cosmology, and in particular introduces the student to what has become known as the ""cosmological standard model"". It discusses the structure and properties of the universe as we observe it today, its evolution and the the underlying physical concepts, and the observations that formed our understanding of the universe.
Assessment: 80% Examination and 20% Coursework Level: 6

Mathematical Techniques 4
SEM1
6
15
Overlap: INK7022U/P Prerequisite: SPA5218 (60% or above) (SPA5304 recommended) Corequisite: None
Prerequisite of: SPA7027U
Description: The module will cover advanced techniques in mathematical physics and will consist of three parts. The first part will cover topics in the general area of analysis such as Fourier Transforms, differential equations, special functions, asymptotic series, complex analysis. The second will cover groups, algebra and representations. The third will cover elements of gepmetry, differential forms, homology, topological invariants.
Assessment: 60% Examination and 40% Coursework Level: 6

Statistical Data Analysis
SEM1
6
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: This course will review basic metrics and techniques used to describe ensembles of data such as averages, variances, standard deviation, errors and error propagation. These will be extended to treat multidimensional problems and circumstances where observables are correlated with one another. The Binomial, Poisson, and Gaussian distributions will be discussed, with emphasis on physical interpretation in terms of events. Concepts of probability, confidence intervals, limits, hypothesis testing will be developed. Optimization techniques will be introduced including chi^2 minimisation and maximumlikelihood techniques. A number of multivariate analysers (sample discriminants) will be discussed in the context of data mining. These will include Fisher discriminants, multilayer perceptron based artificial neural networks, decision trees and genetic algorithms.
Assessment: 80% Examination and 20% Coursework Level: 6

Fluid Dynamics
SEM1
6
15
Overlap: None
Prerequisite: None
Corequisite: None
Assessment: 80% Examination and 20% Coursework Level: 6

Quantum Mechanics B
SEM1
6
15
Overlap: None
Prerequisite: SPA5218 (MO has discretion)
Corequisite: None
Prerequisite of: SPA7029U/P; SPA7031U
Description: This module is both an introduction and revision, followed by an extended exposition of the basic principles and applications of quantum mechanics. Topics include: Operators and the general structure of quantum mechanics, observables, orthonormality of eigenstates, expansion theorem, commuting operators, theory of measurement; The harmonic oscillator; Angular momentum theory, the rigid rotator and applications to rotationvibration spectra of diatomic molecules; Spin in quantum mechanics illustrated with spin1/2: matrix representations, SternGerlach experiments and measurement theory exemplified; Indistinguishable particles in quantum mechanics: Bosons and Fermions; Spherically symmetric potentials and the Hydrogen atom.
Assessment: 85% Examination and 15% Coursework Level: 6

Cosmology
SEM1
7
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: Cosmology is a rapidly developing subject that is the focus of a considerable research effort worldwide. It is the attempt to understand the present state of the universe as a whole and thereby shed light on its origin and ultimate fate. Why is the universe structured today in the way that it is, how did it develop into its current form and what will happen to it in the future? The aim of this module is to address these and related questions from both the observational and theoretical perspectives. The module does not require specialist astronomical knowledge and does not assume any prior understanding of general relativity.
Assessment: 90% Examination and 10% Coursework Level: 7

Relativistic Waves and Quantum Fields
SEM1
7
15
Overlap: None
Prerequisite: SPA5304, SPA6325 & SPA5218
Corequisite: SPA7027U; SPA7024U/P Prerequisite of: SPA7001U/P; SPA7032U/P
Description: This module provides a first introduction into the unification of last century's groundshaking revolutions in physics: Special Relativity and Quantum Mechanics. Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretations of their solutions are analyzed. Students will learn about the fundamental concepts of quantum field theory, starting with classical field theory, quantisation of the free KleinGordon and Dirac field and the derivation of the Feynman propagator. Then interactions are introduced and a systematic procedure to calculate scattering amplitudes using Feynman diagrams is derived. Finally, the quantisation of the electromagnetic field is discussed and the relativistic cross sections for various physically relevant examples are calculated.
Assessment: 90% Examination and 10% Coursework Level: 7

Relativity and Gravitation
SEM1
7
15
Overlap: None
Prerequisite: SPA6308 or equivalent introductory courses
Corequisite: None
Description: This module offers an explanation of the fundamental principles of General Relativity. This involves the analysis of particles in a given gravitational field and the propagation of electromagnetic waves in a gravitational field. The derivation of Einstein's field equations from basic principles is included. The derivation of the Schwarzchild solution and the analysis of the Kerr solution inform discussion of physical aspects of strong gravitational fields around black holes. The generation, propagation and detection of gravitational waves is mathematically analysed and a discussion of weak general relativistic effects in the Solar System and binary pulsars is included as a discussion of the experimental tests of General Relativity.
Assessment: 90% Examination and 10% Coursework Level: 7

Research Methods for Astrophysics
SEM1
7
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: Research in astrophysics builds on a vast body of literature and archived data. This module is an introduction to research methods which exploit existing information sources in astrophysics. The module serves as preparation for the research project which forms a major part of the MSc programme. In this module students will learn how to review and evaluate with critical insight, the current state of research of a chosen area in astrophysics. They will receive training in writing academic reports in an appropriate style, and will learn how to convey research material in a presentation. Additional topics will be included so that students are prepared for project work at an advanced level. These can include specific exercises in using astronomical data archives, scientific word processing, mathematical skills, using mathematical and data analysis packages, project planning, etc.
Assessment: 90% Examination and 10% Practical Level: 7

Solar System
SEM1
7
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: As the planetary system most familiar to us, the Solar System presents the best opportunity to study questions about the origin of life and how enormous complexity arise from simple physical systems in general. This module surveys the physical and dynamical properties of the Solar System. It focuses on the formation, evolution, structure, and interaction of the Sun, planets, satellites, rings, asteroids, and comets. The module applies basic physical and mathematical principles needed for the study, such as fluid dynamics, electrodynamics, orbital dynamics, solid mechanics, and elementary differential equations. However, prior knowledge in these topics is not needed, as they will be introduced as required. The module will also include discussions of very recent, exciting developments in the formation of planetary and satellite systems and extrasolar planets (planetary migration, giant impacts, and exoplanetary atmospheres).
Assessment: 90% Examination and 10% Coursework Level: 7

Stellar Structure and Evolution
SEM1
7
15
Overlap: None
Prerequisite: None
Corequisite: None
Description: Stars are important constituents of the universe. This module starts from well known physical phenomena such as gravity, mass conservation, pressure balance, radiative transfer of energy and energy generation from the conversion of hydrogen to helium. From these, it deduces stellar properties that can be observed (that is, luminosity and effective temperature or their equivalents such as magnitude and colour) and compares the theoretical with the actual. In general good agreement is obtained but with a few discrepancies so that for a few classes of stars, other physical effects such as convection, gravitational energy generation and degeneracy pressure have to be included. This allows an understanding of premain sequence and dwarf stages of evolution of stars, as well as the helium flash and supernova stages.
Assessment: 90% Examination and 10% Coursework Level: 7

Functional Methods in Quantum Field Theory
SEM1
7
15
Overlap: None
Prerequisite: SPA5304 and SPA7018 or equivalent
Corequisite: None
Description: The module will introduce Feynman's path integral formulation of Quantum Mechanics and apply it to study of Quantum Field Theory (QFT). Emphasis will be given to the role of symmetries (Ward identities), the renormalisation group and the idea of effective action. The concept of Wilson's effective action and the different nature of (ir)relevant/marginal terms will be discussed. Simple scalar theories will provide the example where to apply the concepts and the techniques introduced. The course will also touch on some more advanced topics, such as quantum anomalies and conformal field theories.
Assessment: 90% Examination and 10% Coursework Level: 7

Differential Geometry in Theoretical Physics
SEM1
7
15
Overlap: None
Prerequisite: SPA6324; SPA6308 or equivalent
Corequisite: SPA7018U
Description: The aim of this course is to complement the core Relativistic Waves and Quantum Fields (RWQF) module by providing the student with some advanced tools essential for research in modern Theoretical Physics. Using the same starting point as RWQF, Maxwell's theory of electromagnetism, we will focus on the Lagrangian formulation of the two most prominent theories of our time: YangMills (gauge) theory and gravity. The alternative notation of differential forms will be explored and the geometric aspects of gauge theory emphasised. Building on this, and introducing elements from group theory and fibre bundles we will introduce classical solitons as localised, finite energy solutions to the classical field equations in various dimensions (kinks in 2d, vortices in 3d, monopoles in 4d, instantons in Euclidean 4d) and discuss their properties, including the existence of zeromodes, associated collective coordinates and moduli spaces.
Assessment: 90% Examination and 10% Coursework Level: 7
