School of Physical and Chemical Sciences BSc Module Index

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.

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 self-paced programmed learning, with assessment by coursework and an end of year examination.

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.

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 particle-like properties of waves, and wave-like 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.

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 problem-solving.

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.

Description: A module describing sub-atomic 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.

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 1-D quantum wells. (ii)Finite 1-D 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.

Description: This module provides a general introduction to numerical problem solving with the programming language Python. Scientific computing provides an inherently interdisciplinary approach to problem solving; one that combines aspects of applied mathematics, computer science, and software engineering with concepts and models from the physical sciences.

In this module basic aspects of scientific computation, including computer number representations, machine precision, discretisation of equations, error and uncertainty, will be discussed. The mathematical underpinnings of numerical methods of problem solving will be developed, including numerical integration and differentiation, searching, data fitting, interpolation, matrix computing, and solving differential equations.

These theoretical topics will be put into practice during weekly computational laboratory exercises where computer programs will be written that utilise a variety of numerical techniques to solve problems. Authentic examples from the physical sciences and industry and will be explored.

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.

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; space-time diagrams being are used extensively. The course includes discussion of the big bang and black holes.

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.

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.

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 multi-dimensional 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 maximum-likelihood techniques. A number of multivariate analysers (sample discriminants) will be discussed in the context of data mining. These will include Fisher discriminants, multi-layer perceptron based artificial neural networks, decision trees and genetic algorithms.

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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 rotation-vibration spectra of diatomic molecules; Spin in quantum mechanics illustrated with spin1/2: matrix representations, Stern-Gerlach experiments and measurement theory exemplified; Indistinguishable particles in quantum mechanics: Bosons and Fermions; Spherically symmetric potentials and the Hydrogen atom.

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.

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 Klein-Gordon 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 electro-magnetic field is discussed and the relativistic cross sections for various physically relevant examples are calculated.

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.

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.

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).

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 pre-main sequence and dwarf stages of evolution of stars, as well as the helium flash and supernova stages.

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.

Description: The role and characteristics of fields, in particular gravitational and electromagnetic fields. The description of natural phenomena and the widespread occurrence of oscillations and wave motion, with examples taken from the physics of sound and light.

Description: Aspects of electrical theory (current and charge, resistance, capacitors, circuits and meters); atomic structure and properties of the electron; the nucleus, radioactive decay and nuclear energy; introduction to quantum physics.

Description: The module is a broad survey of Astronomy aiming to acquaint you with evolution of the universe and its constituents. A particular theme is the role played by the known laws of physics in understanding astronomical observation. You will: (i) gain a familiarity with the constituents of the observed universe; (ii) appreciate, and be able to explain, the important part played by the laws of physics in designing observations, and in interpreting and understanding them; (iii) be able to explain the different types of information obtainable from observations across the entire electromagnetic spectrum from gamma rays to radio waves.

Description: Further techniques of mathematics needed in the physical sciences. Complex numbers and hyperbolic functions. Polar and spherical coordinates and coordinate transformations. Multiple integrals. Line and surface integrals. Vector calculus. The theorems of Gauss, Green and Stokes. Matrices. Determinants. Eigenvalues and eigenvectors. Fourier series and transforms including the convolution theorem. Differential equations. Exercise classes enable the students to learn practical approaches to problem solving while applying the concepts and techniques introduced in lectures.

Description: An introduction to the basic laws of electromagnetism: electric force and field; electric potential and energy; capacitance; electromotive force; magnetic force and field; the Lorentz force; electromagnetic induction; mutual and self inductance; magnetic energy; LC circuits; Maxwell's equations; introduction to electromagnetic waves; applications in science and engineering.

Description: This course aims to illustrate some important aspects of physics through experimental measurements. The course will be marked by continuous assessment of student laboratory notebooks, which will not be allowed to be removed from the laboratory. Students will perform a number of experiments over the term and will then have to write a scientific paper on one of the experiments that they have performed. The experiments are: Alpha particle spectroscopy; Thermal equation of state and critical point of ethane, Hall effect measurement of germanium; Building a Helium Neon Laser; Nuclear Magnetic Resonance; Building a Michelson Interferometer and measuring the magnetostriction of metals and the refractive index of air; X-ray diffraction spectroscopy; The Zeeman effect.

Description: The course is aimed at giving a coverage of electromagnetic wave theory and of optics. It will act as a bridge between a first year course of introductory electromagnetism and a course on vibrations and waves to give an understanding of optics in terms of electromagnetic waves.

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Description: Introduction to Lagrangian and Hamiltonian formulations of Newtonian mechanics. Origin of Conservation Laws and their relation to symmetry properties. Rotational motion of rigid bodies, Euler's equations, principal axes and stability of rotation, precession. Small vibration approximation, normal modes.

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.

Description: Ever since the dawn of civilisation human beings have charted the paths of the planets across the night sky and speculated about their nature. Indeed the word planet has its origin in the ancient Greek term `planete' meaning wanderer. Used in its modern scientific context the word planet refers to an object which orbits about a star, but which itself is not a star. Planets have a special philosophical significance since they are the bodies on which life itself is expected to come into existence. This course provides an in depth description of our current knowledge and understanding of the planets in our Solar System, and of the planetary systems now known to orbit around stars other than the Sun and the extrasolar planets. The properties of individual planets and their satellites will be described and contrasted, and basic physical principles will be used to explain their orbits and physical features. Our understanding of how planetary systems form will be explored, and current scientific ideas about the origin of life will be discussed.

Description: Galaxies are the building blocks of the universe and deserve the extensive study they now enjoy. This course applies basic physical ideas to astronomical observations, exploring the properties of galaxies themselves and the evolution of structure in the universe.

Description: The module will give you a grounding in the more formal and axiomatic approach to quantum mechanics and introduce you to the application of these tools in the quantum mechanical description of symmetries in particle physics. Topics include: Dirac notation; Hilbert space; linear operators; formal axioms of quantum mechanics; Schoedinger and Heisenberg pictures; harmonic oscillator; raising and lowering operators; time independent perturbation theory; transformation operators; translations and rotations of coordinates; conservation laws and good quantum numbers; rotation operators; angular momentum operators.

Description: Starting from the atomic and quantum descriptions of matter the module uses statistical principles to explain the behaviour of material in bulk. It thus relates microscopic to macroscopic quantities and provides a microscopic explanation of thermodynamics. It provides the bridge between microscopic quantum physics and the behaviour of matter as we know it daily.

Description: This module gives a broad exposition of the modern frame work for the unification of special relativity and quantum theory -- relativistic quantum field theory (QFT). Lagrangian formulation and canonical quantisation of free fields with spin = 0, 1/2, 1 are revised. The construction of interacting quantum field theories is devoloped with special focus on phi^4-theory and quantum electrodynamics (QED). Perturbation theory in terms of Feynman diagrams is developed systematically, and important concepts such as regularisation and renormalisation are introduced. These tools are applied to the calculation of simple tree-level and one-loop S-matrix elements and cross-sections in phi^4 theory and QED, corrections to the electron magnetic moment and the running coupling. The course will also touch on more advanced topics such as anomalies, non-Abelian gauge theories, and modern methods for the calculation of S-matrix elements.

Description: A plasma is an ionized gas where the magnetic and electric field play a key role in binding the material together. Plasmas are present in almost every astrophysical environment, from the surface of pulsars to the Earth's ionosphere. This module explores the unique properties of plasmas, such as particle gyration and magnetic reconnection. The emphasis is on the plasmas found in the Solar System, from the solar corona and solar wind to the outer reaches of the heliosphere and the interstellar medium. Fundamental astrophysical processes are explored, such as the formation of supersonic winds, magnetic energy release, shock waves and particle acceleration. The module highlights the links between the plasmas we can observe with spacecraft and the plasmas in more distant and extreme astrophysical objects.

Description: This module is an introduction to understanding the origin, propagation, detection and interpretation of electromagnetic (EM) radiation from astronomical objects. In this module students will learn: how to describe EM radiation and its propagation through a medium to an observer; the main processes responsible for line and continuum emission and how they depend on the nature and state the emitting material; the effects of the earth's atmosphere and the operation of the detection process at various wavelengths. The material will be illustrated by examples from optical, infrared and radio portions of the EM spectrum.

Description: Ever since the dawn of civilization human beings have speculated about the existence of planets outside of the Solar System orbiting other stars. The first bona fide extrasolar planet orbiting an ordinary main sequence star was discovered in 1995, and subsequent planet searches have uncovered the existence of more than one hundred planetary systems in the Solar neighbourhood of our galaxy. These discoveries have reignited speculation and scientific study concerning the possibility of life existing outside of the Solar System. This module provides an in depth description of our current knowledge and understanding of these extrasolar planets. Their statistical and physical properties are described and contrasted with the planets in our Solar System. Our understanding of how planetary systems form in the discs of gas and dust observed to exist around young stars will be explored, and current scientific ideas about the origin of life will be discussed. Rotationally supported discs of gas (and dust) are not only important for explaining the formation of planetary systems, but also play an important role in a large number of astrophysical phenomena such as Cataclysmic Variables, X-ray binary systems, and active galactic nuclei. These so-called accretion discs provide the engine for some of the most energetic phenomena in the universe. The second half of this module will describe the observational evidence for accretion discs and current theories for accretion disc evolution.

Description: The module considers in detail the basic physical processes that operate in galaxies, using our own Galaxy as a detailed example. This includes the dynamics and interactions of stars, and how their motions can be described mathematically. The interstellar medium is described and models are used to represent how the abundances of chemical elements have changed during the lifetime of the Galaxy. Dark matter can be studied using rotation curves of galaxies, and through the way that gravitational lensing by dark matter affects light. The various topics are then put together to provide an understanding of how the galaxies formed.

Description: This module covers advanced concepts of modern cosmology, and in particular will introduce the student to cosmological perturbation theory. It discusses the observed structure of the universe, how these structures formed, and how they can be used to test our theories and models of the universe. The module will also discuss recent and upcoming experiments and large scale structure surveys and their relevance for cosmology.

Description: This course introduces core concepts in supersymmetry that can be applied to quantitatively understand a broad variety of physical systems and is a complement to the AQFT and FMQFT modules. Starting with supersymmetric quantum mechanics as a toy model, the course covers the supersymmetry algebra, its representations, the Witten Index, and the resulting constraints on quantum dynamics. We then move on to introduce supersymmetric field theories in three space-time dimensions consisting of scalars and fermions while giving a basic introduction to symmetry currents, the classical and quantum Wilsonian renormalization group flow, moduli spaces, spurions, and non-renormalization arguments. The course culminates in a study of simple dualities in three-dimensional supersymmetric abelian gauge theories. We conclude with a discussion of supersymmetry in four space-time dimensions and, time permitting, the embedding of our constructions in string theory.

Description: The module will cover the basics of string theory including the classical relativistic physics of the string, its quantisation and the resulting spectrum. This will then be extended to examine so called p-branes and the basics of M-theory.

Description: You will initially register for the extended project PHY776. This module provides you with the experience of working, independently, on a problem within physics (often using the resources found within a research group of the department). These may be problems in experimental, computational or theoretical physics or a project in astronomy. A list of projects is available on the extensive projects homepage containing a brief description of the projects on offer and the supervisors of those projects. You shall arrange a project by reading these pages and meeting with potential supervisors. Associated with the project is a weekly mandatory seminar to which you will occasionally be expected to contribute. In the light of adequate progress during the first semester you may, after producing a report, be relegated to a 15 credits Independent Project following careful consideration by a panel of staff (Supervisor, CO and DCO).

Description: You will examine a specialised area of physics by directed reading and independent study. You will learn to use scientific research literature databases. You will develop the skill of writing a scientific review summarising current knowledge in a field of physics. You may enrol for this project only with the permission of the Module Organiser for MSci projects. Open only to 3rd year MSci students.

Description: The MSc project involves a critical review of a chosen topic in modern astrophysics, and may include some original research. Students write a dissertation summarising current research in that chosen field and the extent of their own investigations.

Description: The MSc research Project is at the heart of the MSc programme. It is an independent project undertaken by the student within a working research group in the School. The project runs over three semesters in order to allow for the student to both design their project (using available literature etc.), be trained in the relevant techniques and carry out a reasonably substantial piece of research based on an actual (real) research problem. The presentation of the student findings is based both on a formal, technical written report (75 page maximum length) and on an oral presentation (e.g. powerpoint talk) and examination.

Description: PA student will develop design, experimental, computational or analytical skills through the independent study of a problem in physics. S/he will learn to write a scientific report summarising results of an independent investigation and placing them in a physics context. The project will run through both semesters and will involve keeping a research log (see 'Engagement Log' elsewhere on this page), interim coursework, a final written report and oral assessment at the end of semester B.
The aim of the investigative project is to give the student the opportunity to work independently on a chosen project towards specified goals. These goals will vary from project to project and may include: writing software to achieve a specified computational task, e.g., simulation of a physical process; carrying out a series of measurements to establish or disprove a working hypothesis; building a piece of equipment, e.g., to interface an experiment to a PC; analytical mathematical analysis applied to the study of a theoretical problem.

Description: The MSc project involves a critical review of a chosen topic in modern astrophysics, and may include some original research. Students write a dissertation summarising current research in that chosen field and the extent of their own investigations.

Description: Students will develop design, experimental, computational or analytical skills through the independent study of a problem in physics. They will learn to write a scientific report summarising results of an independent investigation, placing them in a physics context, and detailing the methods used and the results obtained. The project will run through both semesters and will involve a report and an oral presentation.