Physics with Theoretical Astrophysics MSci

How does the world really work?

We’ll take you from Newton’s mechanics, the pinnacle of the scientific revolution and the foundation of our understanding of modern physics, right through to our current understanding of physics with Einstein’s theory of relativity and quantum mechanics.

This module will underpin your entire physics degree. It contains all the ideas and principles that form the basis of our modern world. As you’ll find out, some of these ideas are very strange indeed.

You’ll study:

• Newton’s laws of mechanics
• The physics of waves and oscillations
• Electricity and magnetism
• Quantum mechanics and the foundations of modern physics
• Einstein’s relativity

You’ll receive training in basic computing techniques using Python, and will be introduced to their use in solving physical problems.

You’ll spend two hours in computer classes and a one hour lecture each week. 

In this module you will receive: an introduction to the basic techniques and equipment used in experimental physics; training in the analysis and interpretation of experimental data; opportunities to observe phenomena discussed in theory modules and training in the skills of record keeping and writing scientific reports.

This module will teach you how the basic principles of physics are applied in a range of situations and provide you with knowledge of the primary mathematical methods for the analysis of physical problems. On completion of the module, you will be able to formulate problems in physics using appropriate mathematical language. 

This module will cover major areas at the forefront of modern research, beyond those encountered in the core modules. You’ll be introduced to cutting-edge topics in medical physics, nanoscience, and astronomy by experts in each of these fields.

The frontiers of knowledge in physics are constantly changing. This module will cover major areas at the forefront of modern research, beyond those encountered in the core modules. You’ll be introduced to cutting-edge topics in medical physics, nanoscience, and astronomy by experts in each of these fields.

You’ll study:

• Medical physics: the physics of sound and hearing; radioactivity in medicine; magnetic resonance imaging
• Nanoscience: physics at the nanoscale; introduction to quantum mechanics; viewing and manipulating matter at the atomic level; chaos
• Astronomy: stars, galaxies, and black holes; gravitational waves; the Big Bang; climate change

This year-long module covers the mathematical background required for the majority of undergraduate-level study of physics and astronomy. It will complement the material studied in other first-year physics degree modules.

The structure of the module has been designed to ease students into the level of maths required for the early stages of your degree. 

The topics covered in this module are:

• Complex numbers
• Differentiation and Taylor Series representations
• Stationary points of two-dimensional functions
• Integration techniques for functions of single and multiple variables
• Partial derivatives of functions of multiple variables
• Conic sections in plane geometry
• Fourier representation of functions and the Fourier transform
• Matrices and eigenvalue problems
• Solving first-order ordinary differential equations (ODEs)
• Solving homogeneous and inhomogeneous linear constant coefficient ODEs

This module will introduce you to the mathematical language behind the classical mechanics describing our universe. You will learn about Lagrangians and Hamiltonians, the starting place from which we can determine the dynamics of complicated systems, like pendula and planets orbiting the sun, as well as the origin of conserved quantities such as energy and momentum.

This is a fun module. At school you learnt Kepler’s Laws, Newton’s Law of Gravity, and F=ma, but how can you derive these amazing results? Where do they come from?

Here you will find out, as we introduce you to the mathematical language behind the classical mechanics describing our universe. You will learn about Lagrangians and Hamiltonians, the starting place from which we can determine the dynamics of complicated systems, like pendula and planets orbiting the sun, as well as the origin of conserved quantities such as energy and momentum. For two hours a week we will take you into the mathematics and ideas of giants like Newton, Euler, Lagrange, Noether and Hamilton.

Among many exciting things, you will study:

• Newton’s Laws and deriving the orbits predicted by Kepler
• Lagrangians and Hamiltonians, the building blocks behind classical mechanics
• The Euler-Lagrange equations describing the dynamics behind classical systems
• Rigid bodies – introducing moments of inertia, centre of mass and more so that we can apply these results to many particle rigid systems, like pendulums and even you
• Constraints – how to determine the dynamics of a system where it is constrained, for example, the motion of an explorer constrained to be on the surface of the earth
• The motion of charged particles, like electrons in an electromagnetic field
• Hamilton’s equations as an alternative way to determine the dynamics of a system, particularly useful when we are searching for conserved quantities like angular momentum
• Spinning tops – what? You heard right, the vital roles of gyroscopes in our life are understood by 5-year-olds, but the mathematics certainly is not. Thanks to this course, now you can understand that as well.

This module provides an introduction to the theory and elementary applications of quantum mechanics, a theory that is one of the key achievements of physics. Quantum mechanics is an elegant theoretical construct that is both beautiful and mysterious. Some of the predictions of quantum mechanics are wholly counter-intuitive and there are aspects of it that are not properly understood. Nonetheless, it has been thoroughly tested empirically for nearly a century and, wherever predictions can be made, they agree with experiment.

The notes, videos, and simulations for the first semester of The Quantum World are all publicly available and freely accessible. Check out the notes online, which include embedded links to the videos and interactive simulations.

You’ll study:

• Quantum vs classical states
• Fourier series and transforms: translating from position to momentum space
• The Heisenberg uncertainty principle (particularly from a Fourier perspective)
• The time-dependent and time-independent Schrödinger equation
• Bound and unbound states, scattering and tunnelling
• Wavepackets
• The subtleties of the particle in a box
• Operators, observables, and the thorny measurement problem
• Matrix mechanics and Dirac notation
• The quantum harmonic oscillator
• Conservation and correspondence principles
• Angular momentum
• Stern-Gerlach experiment
• Spin
• Zeeman effect, Rabi oscillations
• 2D and 3D systems
• Degeneracies
• Hydrogen atom and the radial Schrödinger equation
• Entanglement and non-locality
• ... and, of course, that ever-frustrating feline...

The physics of waves features in our everyday lives. Waves are important phenomena. They include:

• electromagnetic waves that we know as light
• communication via radio and microwaves
• surface waves on water
• shock waves in earthquakes

Understanding light and how it can be manipulated leads to important technical applications such as optics and cameras in mobile phones, telecommunication and the internet or even quantum computers.

This module will cover the wave description of light; geometrical optics and imaging, interference and diffraction; optical interferometry. The second half of the module will introduce more general methods for the discussion of wave propagation, and Fourier methods.

You’ll study:

• Imaging and matrix methods
• Microscopes and telescopes. State of the art telescopes such as the Hubble Telescope, the VLT (Very Large Telescope) and the James Webb Telescope.
• Interference patterns and their applications, for example to study the structure of proteins, of crystals and of fullerenes

Macroscopic systems exhibit behaviour that often differs from that of their microscopic constituents. This module explores the relationship between the macro and micro worlds, and the complexity which emerges from the interplay of many interacting degrees of freedom.

You’ll study:

• Laws of thermodynamics, and how they are still relevant
• Macroscopic characterisation of matter, for example how liquid nitrogen is made and understood
• Statistical formulation, linking micro and macro systems
• Quantum statistics, providing a theory for everything!

In this module you will explore the concepts of scalar and vector fields. You will learn the mathematics of vector calculus, which give us a powerful tool for studying the properties of fields and understanding their physics.

You will then study its application in two important and contrasting areas of physics: fluid dynamics, and electromagnetism. We use examples such as water draining from a sink or wind in a tornado to provide intuitive illustrations of the application of vector calculus, which can then help us to understand the behaviour of electric and magnetic fields.

You’ll study:

• The fundamental principles and techniques of vector calculus, and methods to visualise and calculate the properties of scalar and vector fields
• The application of vector calculus to fluid flow problems
• Maxwell’s equations of electrodynamics, and their applications in electrostatics, magnetic fields and electromagnetic waves.

This module introduces a range of theoretical techniques for the construction and analysis of simplified effective models. You will learn advanced mathematical methods and apply them to problems in quantum mechanics, electromagnetism, and other areas of physics.

You’ll study:

• Differential calculus of complex functions
• Advanced solution methods for differential equations such as the Schrödinger equation
• Vector spaces of functions and Green functions

In this module you will learn how the same physics that works on Earth – gravity, electromagnetism, thermodynamics, optics, quantum physics, atomic and nuclear physics – is used to understand stars. You will explore the most important physical processes occurring in stars of different types. You will then use this knowledge to build mathematical models of stars and to understand their internal structure, their formation, evolution, and death.

You’ll study:

• How astronomers measure the most important properties of stars such as their mass, size, distance, brightness, temperature, chemical composition and age. This module will then teach you how physics is able to explain these properties.
• How energy is generated inside stars through nuclear fusion, and how it is transported to the surface to make stars shine.
• How to write the equations that describe the structure of stars, and how to use them to build mathematical models that explain their properties and evolution.
• How stars are born, how they evolve with time, how long they live, how they die, and what remnants they leave behind. You will be able to understand, for instance, how supernovae explode and how some black holes form.

This module will develop your current understanding of the various large-scale physical processes that dictate the formation, evolution and structure of galaxies, from when the Universe was in its infancy to the present day.

You’ll explore a range of topics, starting with the fundamentals of observational techniques used by astronomers for understanding the structure of our own galaxy, the Milky Way. We will then look at the more sophisticated ways of unpicking the physics that drives the complexity we see throughout the population of galaxies in the Universe.

Specifically, in this module, you will study:

• The structure of the Milky Way – how we determine the structure of the Milky Way, its rotation curve and what this implies for its dark matter content
• Properties of galaxies in the Universe – how astronomers classify galaxies, the properties of the different classes and how their constituents vary between classes
• Dynamics of galaxies – kinematics of the gas and stars in galaxies, why spiral arms form, the theory of epicycles, bar formation, different types of orbits of matter within galaxies
• Active galaxies – radio galaxies, quasars and active galactic nuclei, super-massive black holes
• The environment of galaxies – how the environment that a galaxy resides in affects its evolution and structure
• Galaxy evolution – observations of galaxy evolution from the early Universe to the present day, models of galaxy evolution.

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.

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.

Understanding the dynamics of quantum systems is crucial, not just for describing the fundamental physics of atoms, but also for the development of exciting new quantum-based technologies. This module will equip you with the key theoretical concepts and methods needed to explore how quantum systems evolve with time.

You’ll study:

• Connections between the dynamics of quantum systems and that of more familiar classical ones
• When (and how) to use approximations that allow complex problems to be made much simpler
• The extent to which the evolution of quantum states can be controlled
• How to put theory into practice using one of IBM’s prototype quantum computers.

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 will work in pairs and are 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. You will also be required to maintain a diary/laboratory notebook throughout.

Occasionally the work from these projects is used in scientific publications, and the students involved are named as authors on those publications.

Depending upon the type of project that you decide to do, you will design and carry out your own experiments, theoretical calculations or computational work and use them to generate what are often new and interesting results. The project culminates in your writing a scientific report which is submitted for assessment along with your laboratory notebook.

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

Symmetry plays a central role in physics. Most of the fundamental Laws of modern physics have been formulated using symmetry principles. Symmetry is also expected to guide for further understanding and development of theories of physical phenomena.

Through a combination of lectures, engagement sessions and workshops, this module equips you with:

• the key concepts of symmetry
• the correspondence between symmetries and conservation laws
• the derivations of physics laws from the action principles
• and the consequences of symmetry breaking.

You’ll study:

• Symmetries of space and phase space using classical mechanics
• Symmetries of spacetime and in electromagnetism using special relativity
• Main symmetry groups of modern physics laws
• How structures in nature are results of symmetry breaking.

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.

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

In this year-long module you’ll work on an original theoretical or practical problem directly relevant to the research taking place in the school or in a collaborating external organisation, such as industry or an overseas university. You’ll spend semester one researching the background to your chosen project and carry out your original research in semester two.

You’ll:

• Choose a project from a wide range of options reflecting the broad range of research in the school (Astronomy; Particle Cosmology; MRI; Experimental and Theoretical Condensed Matter Physics)
• Study the background and underlying physical principles of your choice
• Carry out the original research and present your results orally and in a written report

After more than 200 hundred years of Newtonian gravity, Einstein revolutionised the way we view space and time. This module will introduce you to the key concepts and tools used to describe gravitational physics as set down in General Relativity.

You’ll study:

• How geometry plays a central role in physical measurements
• How to compute the paths of objects in curved spacetime
• The spacetime geometry of black holes

This module develops a range of modern astronomical techniques through student-centered approaches to topical research problems. You’ll cover a range of topics related to ongoing research in astronomy and astrophysics, and will encompass theoretical and observational approaches. This module is based on individual and group student-led activities involving the solution of topical problems including written reports and exercises, and a project.

This module introduces you to the key ideas behind modern approaches to our understanding of the role of inflation in the early and late universe, in particular through the formation of structure, the generation of anisotropies in the cosmic microwave background radiation, and the origin of dark energy. You’ll study through a series of staff lectures and student-led workshops.

Modern science is data rich. For example, it’s not uncommon for a single experiment to generate terabytes, or even petabytes of data. As scientists, one of the major challenges we face is to collapse these vast data archives into meaningful information that we can understand, and use to draw conclusions.

In this module, you will learn the critical mathematical techniques that are used to do this. We will cover techniques from simple image processing, all the way to advanced blind source separation and machine learning. You will then put these techniques into practice, in a data processing project that may range from satellite imaging to measuring the amount of information stored by the human brain.

This module will develop the modern theoretical description of phase transitions and critical phenomena and provide an introduction to the dynamics of non-equilibrium systems. Topics to be covered will include:

 • ordered phases of matter;

 •  order parameters;

 •  scaling behaviour at critical points;

 •  mean-field approaches;

 •  finite-size scaling;

 • stochastic processes;

 • Langevin dynamics and the Fokker-Planck equation.
Applications, both within and beyond, condensed matter physics will be discussed.

Electronic devices such as transistors and light emitting diodes are the basic building blocks of the technology that underpins all aspects of the modern world.

Previous modules on Solid State Physics and Semiconductor Physics should have given you a good understanding of how these devices work. The move to make these building blocks ever smaller leads us into regimes where we have to treat the quantum nature of electrons in solids much more seriously.

Research in this area has led to the development of entirely new types of electronic devices such as quantum well lasers. It has also uncovered entirely new physical phenomena like the quantum Hall effects. It is this new physics and its applications that is the topic of this module.

You will study:

• The quantum theory of electrical transport in solids – elastic and inelastic scattering, conductance quantization
• Quantum confinement – technology for producing 2d, 1d and 0d electronic systems
• Quantum interference phenomena – weak and strong localization, Aharonov Bohm effect
• Carbon Nanotubes and Graphene
• Quantum Dots – tunnelling, charging effects, optoelectronic applications
• Quantum Hall Effects and Topological Insulators.