Physics with Theoretical Physics BSc

You’ll study a selection of mathematical techniques that are used for analysing physical behaviour. Topics will include:

• complex numbers
• calculus of a single variable
• plane geometry
• differential equations
• calculus of several variables
• matrix algebra

You’ll spend around three hours per week in workshops and lectures studying this module.

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

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 year-long module will train you in the mathematical modelling of physical processes. You’ll cover topics such as basic statistics and errors, dimensional analysis, curve sketching, orders of magnitude and estimates, and integrating problems in physics among others.

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. 

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...

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.

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

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. 

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.

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

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.

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

We will study some of the fundamental forces at the nanoscale and look at the role of key concepts such as entropy. We will also learn how we can visualise and measure the nanoscale structures that form.

The nanoscale world is very different from our regular experience. Thermal energy pushes and pulls everything towards a state of disorder whilst nanoscale forces allow for materials to resist this and stay together. We will study some of the fundamental forces at the nanoscale and look at the role of key concepts such as entropy. We will also learn how we can visualise and measure the nanoscale structures that form.

While the forces we will study operate over distances as small as 1 nanometre we will explore how these concepts are responsible for phenomena in our everyday world we often don’t even think about:

• Why is a droplet spherical?
• What is going on when you scramble an egg?
• How can a gecko walk across a perfectly smooth ceiling?
• Why do you use soap when you wash?
• Why don’t oil and water mix?

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.

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

Science is the cornerstone of modern healthcare. For example, in the UK’s National Health Service (NHS) more than 80% of clinical decisions are informed by scientific analysis.

In this module, we will explore some of the critical technologies that underpin these decisions. The course begins by exploring particle accelerators, and how they are used to create, for example, high energy photons or anti-matter particles. We will then see how these are used to either diagnose or treat illnesses such as cancer.

We will look closely at medical imaging techniques such as X-ray computed tomography (the CT scan), exploring the mathematics of how high-definition images of the body can be formed. We will cover nuclear medicine – how radiation can be used to track the function of organs in the body – and how advanced mathematical models feed into diagnostic decisions. 

The techniques for magnetic resonance imaging (MRI) and spectroscopy (MRS) are explored. The course aims to introduce the brain imaging technique of functional magnetic resonance imaging (fMRI), giving an overview of the physics involved in this technique. The electromagnetic techniques of electroencephalography (EEG) and magnetoencephalography (MEG) will then be outlined, and the relative advantages of the techniques described.

The invention of the scanning tunneling microscope (STM) in the 1980s has led to a revolution in the imaging of surfaces and has provided an enormous stimulus for the development of nanoscience. The operation of a scanning probe microscope relies on the interaction between a local probe and a surface. A family of techniques has been derived from the STM which exploit a range of different forces and other interactions for image formation. The most widely-used of these techniques is atomic force microscopy which, unlike, STM, can be used to image insulating samples. In this module the focus will be on the development of physical models to describe the interaction between a local point-like probe and a surface. The operation of the STM will be considered in detail together with design considerations which are common across all scanning probe microscopes. In the second half of the course, forces between the tip and sample will be considered and methods for measuring these interactions will be discussed. The probe-surface interaction can also be used to modify the surface with a specificity which can result in placement of single atoms and molecules and these patterning processes will be discussed. Throughout the course images from the current research literature will be introduced to inform students of the range of possible applications of this these techniques.

This module explores how physics-based techniques are used to gain insight into complex molecular systems of biological relevance. In studying the physics underpinning this area of research where chemistry, biology and physics all overlap, we will draw on principles derived from quantum mechanics and statistical physics to develop a better understanding of the biomolecular world.

Physics has made significant contributions in our efforts to understand the underlying molecular principles of life. For instance, physics plays an important role in the development of sophisticated methods that make it possible to measure the complex structure of biological molecules and their mutual interactions and dynamics. Two important groups of such biomolecules that will be discussed in the module are proteins and deoxynucleic acids (DNA).

Topics covered in this module include:

• Introduction into the important classes of complex biomolecules
• What are the underlying principles that make molecules to acquire a functional 3-dimensional structure?
• How can molecular structure be measured with high accuracy?
• How do molecular motors work and can molecules carry out directional motion?
• How can molecular forces and distances be measured between individual molecules.

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