Physics with Theoretical Physics - U6UPHYTH

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

In this module, you’ll develop your knowledge, understanding and problem-solving skills across several core areas of physics, including:

• classical mechanics
• relativity
• vibrations and waves
• quantum physics
• thermal physics

You’ll further explore how these theoretical principles explain a wide range of natural phenomena and examine their relevance to modern technological applications. 

This module builds on your foundation in both classical and modern physics, preparing you for more advanced topics and practical application.

In this module, you’ll continue to build your knowledge, understanding and problem-solving abilities in several core areas of physics, including:

• classical mechanics

• relativity

• vibrations and waves 

• quantum physics

• thermal physics

You’ll further explore how these theoretical principles explain a wide range of natural phenomena and examine their relevance to modern technological applications. 

This module builds on your foundation in both classical and modern physics, preparing you for more advanced topics and practical applications. 

New physical laws are discovered, and the consequences of known laws are understood through three main approaches: experimental, computational, and mathematical. This module provides a clear introduction to these methods. This module focuses on experimental and computational physics, along with concepts common to all three approaches.

In the experimental part of the module, you will carry out, record, and report on experiments, developing essential skills and learning standard experimental techniques.

The computational strand introduces you to Python programming for simulating physical models, analysing data and creating visualisations. The discovery strand ties everything together. You will use computational tools to analyse experimental and simulation data, assess and reduce random errors, and learn to communicate your findings clearly in a scientific style.

In this module, you’ll develop essential professional skills for a career in physics. You will focus on:

• professional communication

• teamworking

• professional behaviour and reflective practice

• academic integrity and ethics

• giving, receiving and reflecting on feedback

• equity, diversity and inclusion in physics

Through a series of activities, you’ll explore specialised areas of physics that you’ll study later in the programme, along with broader topics such as sustainability. You will also gain an understanding of how your degree is structured, the research that underpins it and the wide range of career paths available to physicists.

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 begins by developing the mathematical tools needed to describe classical fields, focusing on vector calculus. You will then explore the behaviour of static electric and magnetic fields, their sources, and their effects on charged particles.

The module progresses to dynamic situations where electric and magnetic fields interact, leading to the unified framework of Maxwell’s equations. You will see how these equations describe electromagnetic waves in empty space and apply this understanding to key concepts in optics.

Finally, the module introduces how electromagnetic fields behave in dielectric and magnetic materials, providing a foundation for further study in electromagnetism and optics.

This module builds on Investigations in Physics 1 and follows a similar structure, now focusing on mathematical, computational and discovery skills.

The mathematical aspect expands on techniques from the Mathematical Methods and Modelling for Physicists module. You will learn new methods for modelling physical systems, applying these to specific examples and exploring how models can be tested.

The computational part develops your coding skills further, covering data handling, analysis and modelling. You will work with more advanced data structures, algorithms, library functions, and learn modular design and code integration.

The discovery strand strengthens your abilities in data analysis, introducing more advanced hypothesis testing. You will also refine your skills in scientific report writing and presenting results effectively.

This module provides comprehensive training in three key areas: communicating science in different formats and for various audiences, working effectively in teams and applying practical problem-solving strategies.

You will have the opportunity to practice these skills in a range of settings, including synoptic tasks that integrate knowledge from across the core physics modules.

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...

This module explores the properties of matter across a wide range of scales, covering nuclear and particle physics, atomic physics, and solid state physics.

The focus will be on key concepts and models essential for understanding behaviour at each scale. You will also learn how quantum and statistical physics methods are applied to determine material properties, from microscopic systems to macroscopic bodies.

In the first semester, this module includes lectures, workshops and practical classes. Some sessions build on the "discovery" strand from Investigations in Physics 1 and Investigations in Theoretical Physics modules, while others focus on developing mathematical and computational techniques relevant to the available projects.

In the second semester, you will work in pairs on a theoretical project chosen from a published list, applying the skills and knowledge gained in the first semester.

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.