Mathematical Physics BSc

Solid state physics underpins almost every technological development around us, from solar cells and LEDs to silicon chips and mobile phones.

The aim of this module is to introduce to you the fundamental topics in solid state physics. We start by looking at why atoms and molecules come together to form a crystal structure. We then follow the electronic structure of these through to interesting electronic, thermal and magnetic properties that we can harness to make devices.

You’ll study:

• Why atoms and molecules come together to form crystal structures
• The description of crystal structures, reciprocal lattices, diffraction and Brillouin zones
• Nearly-free electron model – Bloch's theorem, band gaps from electron Bragg scattering and effective masses
• Band theory, Fermi surfaces, qualitative picture of transport, metals, insulators and semiconductors
• Semiconductors – doping, inhomogeneous semiconductors, basic description of pn junction
• Phonons normal modes of ionic lattice, quantization, Debye theory of heat capacities, acoustic and optical phonons
• Optical properties of solids absorption and reflection of light by metals, Brewster angle, dielectric constants, plasma oscillations
• Magnetism – Landau diamagnetism, paramagnetism, exchange interactions, Ferromagnetism, antiferromagnetism, neutron scattering, dipolar interactions and domain formation, magnetic technology

This module will introduce students to the physics of atoms, nuclei and the fundamental constituents of matter and their interactions. The module will also develop the quantum mechanical description of these.

Topics to be covered are:

• Approximation techniques first order perturbation theory, degeneracies, second order perturbation theory, transition rates, time-dependent perturbation theory, Fermi's golden rule
• Particle Physics protons and neutrons, antiparticles, particle accelerators and scattering experiments, conservation laws, neutrinos, leptons, baryons and hadrons, the quark model and the strong interaction, weak interactions, standard model
• Introduction to atomic physics review of simple model of hydrogen atom, Fermi statistics and Pauli principle, aufbau principle, hydrogenic atoms, exchange, fine structure and hyperfine interactions, dipole interaction, selection rules and transition rates
• Lasers optical polarization and photons, optical cavities, population inversions, Bose statistics and stimulated emission, Einstein A and B coefficients
• Nuclear Physics Radioactivity, decay processes, alpha, beta and gamma emission, detectors, stability curves and binding energies, nuclear fission, fusion, liquid drop and shell models.

In this module you will apply the quantum mechanics that you learned in Year 2 to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.

You will carry out a project drawn from one of several areas of physics. The project may be experimental or theoretical in nature. Many of the projects reflect the research interests of members of academic staff. You’ll work in pairs and will be expected to produce a plan of work and to identify realistic goals for your project. Each pair has a project supervisor responsible for setting the project.

10 credits in the Autumn semester.

Content to be confirmed.

In this module you will explore the physics of planets and their atmospheres — a topic that is at the forefront of modern astrophysics and planetary science.

In the last few decades, the discovery of thousands of exoplanets beyond our Solar System has revolutionised the study of planets and their atmospheres.

Closer to home, understanding the physical processes at play in the Earth’s atmosphere remains vital for predicting weather and climate.

You’ll study:

• Exoplanet detection methods and the physics of planet formation
• The structure, temperature and composition of planetary atmospheres
• Atmospheric dynamics
• Exoplanet atmospheres and the search for biosignatures

Cosmology is the scientific study of the Universe as a whole. It aims to understand what the Universe is made of, and its evolution from the Big Bang until today (and into the future).

You’ll study:

• observational evidence for the Big Bang
• how the expansion of the Universe depends on its contents and geometry
• how the contents of the Universe evolve as it expands and cools
• dark matter and dark energy: observational evidence and the latest theoretical models
• inflation, a proposed period of accelerated expansion in the very early Universe

This module explores the physical processes involved in the most extreme environments known in the Universe. Among the objects studied are neutron stars, black holes, supernova explosions, and active galactic nuclei.

How can complicated nonlinear mechanical, electrical and biological systems be understood? In this module you will develop your knowledge of classical mechanics of simple linear behaviour to include the behaviour of complex nonlinear dynamics. You’ll learn about the way in which nonlinear deterministic systems can exhibit essentially random behaviours, and approaches to understand and control them.

You’ll learn:

• In-depth knowledge of nonlinear dynamics in continuous and discrete classical systems
• Practical skills in using analytical, geometric and numerical approaches to analyse dynamics in nonlinear systems of various dimensions
• Methods to understand and create beautiful fractals through simple iteration rules.

This module introduces you to the physics and applications of Semiconductors. Semiconductors are key materials of the current Information Age. They enabled most of the devices and technologies we use everyday, such as computers, internet, mobile phones. Semiconductors help us to mitigate global warming, data theft, end of the Moore’s law and other global challenges.

This module includes detailed overview of the Semiconductors past, present and future, and provides skills and knowledge essential for a future Semiconductor researcher or engineer.

You’ll study:

• Physics and applications of conventional semiconductor materials and devices, for example p-n diodes and field-effect transistors
• Physics and applications of novel semiconductor materials, quantum materials, nanostructures, low dimensional materials, such as graphene and quantum dots
• Current and future semiconductor challenges and technologies, such as efficient solar cells, ultrasensitive phone cameras and quantum computers.

This module aims to provide you with the skills necessary to use computational methods in the solution of non-trivial problems in physics and astronomy. You’ll also sharpen your programming skills through a three hour computing class and one hour of lectures per week. 

Particle physics has been hugely influential in both science and society, from the discovery of the electron to the detection of the Higgs boson. In this module you will be introduced to the mathematical tools required to understand our current description of the Standard Model of particle physics.

You’ll study:

• The Dirac equation, which describes electrons, quarks and neutrinos
• How symmetry and conservation laws are crucial in particle physics
• The Feynman approach to computing the scattering of particles

You will extend your understanding of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases.

Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.

This course introduces various analytical methods for the solution of ordinary and partial differential equations, focussing on asymptotic techniques and dynamical systems theory. Students taking this course will build on their understanding of differential equations covered in Modelling with Differential Equations.

The module introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics. We explore how classical concepts enter quantum mechanics, and how they can be used to find approximate semi-classical solutions.

You will be introduced to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain exciting new phenomena that occur in relativity.

This course consists of a self-directed investigation of a project selected from a list of projects or, subject to prior approval of the School, from elsewhere. The project will be supervised by a member of staff and will be based on a substantial mathematical problem, an application of mathematics or investigation of an area of mathematics not previously studied. Further information will be provided to you on the Moodle page. The course includes training in the use of IT resources, the word-processing of mathematics and report writing.