Students will gain an insight into advanced aspects of electrodynamics and EM wave propagation. Students will investigate the electromagnetic power radiated by an accelerating charge and an oscillating electric dipole, and the EM fields of a relativistic charged particle. The module will also provide an understanding of the behaviour of electromagnetic modes in perfectly conducting rectangular waveguides and cavities, and the propagation of EM waves in a medium.

On completion, students will be able to calculate the power radiated from accelerating charges and oscillating electric dipoles, and will develop an understanding of the mode structure of EM fields in simple bounded regions such as waveguides and cavities.

This module provides students with a working knowledge and understanding of electromagnetism through Maxwell’s equations using the tools of vector calculus. Students will become familiar with the common connections between the many different phenomena in nature that share the mathematical model of a harmonic oscillator or of a wave. The module addresses the basic properties of wave propagation, diffraction and inference, and laser operation.

Students will develop their skills in vector calculus and will learn to apply Maxwell’s equations in the analysis of common electromagnetic phenomena, including motors and generators, and in the fundamental connection between electricity and magnetism. Students will gain practical knowledge of Fresnel and Fraunhofer diffraction, as well as thin-film interference fringes and anti-reflection coatings. Additionally, the module aims to enhance students’ understanding of the origin of polarisation, and the relevance of dichroism, along with an understanding of the basic elements of a laser, laser operation and important features of laser light.

Designed to provide students with a working knowledge of the basic mathematical techniques that are required when studying physics at degree level and beyond, this module’s range of topics include a look at linear algebra, where students will discover coupled linear equations, linear transformations and normal modes of coupled oscillators. A section on Hilbert space will address wave equation, bases of functions and Kronekker delta-symbol, and angular harmonics will be covered in detail.

Over the duration of the module, students will become familiar with Pauli matrices, eigenvalues, eigenvectors and commutation relations, and will develop a range of skills and techniques required for solving various common types of linear equations. Additionally, a workshop led by postgraduate teaching assistants will be held every two weeks to provide extra one-to-one tuition and support with coursework assignments as required.

This module introduces the Fourier series and transforms, and addresses their application to examples in physics. Students will learn how to express a periodic function as a Fourier series, and find the Fourier transform of a function.

Additionally, students will solve linear ODEs and PDEs using Fourier techniques, as well as developing the ability to solve problems with initial conditions and/or spatial boundary conditions.

The module is compulsory in the Theoretical Physics Pathway and optional in Particle Physics and Particle Physics with Cosmology Pathways.

The module develops students’ knowledge of Newton’s laws, central forces, integrals of motion and dynamics and orbits. Students will gain an insight into generalised coordinates and momenta, Hamiltonian function, Poisson brackets and canonical transformations. The module additionally features lectures on important analytical methods used both in classical mechanics and in broader areas of theoretical and mathematical physics.

Students will develop the ability to integrate equations of motion for dynamical problems in classic mechanics, and will have experience in using variational methods, in addition to gaining the knowledge required to relate Hamiltonian and Lagrangian approach to theoretical mechanics and canonical transformations. Students will be able to exploit the generality of Lagrangian and Hamiltonian techniques by using an appropriate generalised coordinates.

This module covers quantum mechanics in all its generality, from its central postulates and mathematical language to concrete phenomena and applications. Students will learn how the main postulates give precise meaning to the states, observables, dynamics, and measurable properties of quantum systems, and how this translates into general features of the theory, such as its inherent probabilistic nature on the one hand, and precise quantisation of observable properties on the other. This material is introduced and developed by a series of model systems and applications, such as the particle in a box, tunneling through a barrier, the harmonic oscillator, the hydrogen atom, angular momentum and spin, driven systems displaying radiative transitions, and many-body systems exhibiting entanglement and obeying the Pauli exclusion principle. Students will also become familiar with the mathematical language of the theory, including the Dirac notation, differential and matrix operators, commutation relations, and the role of eigenvalue problems. They will also gain practice with solution techniques such as separation of variables, stationary and time-dependent perturbation theory, the Ehrenfest and Heisenberg picture. Through further applications and examples, students will acquire prerequisite knowledge for advanced courses in atomic and molecular physics, condensed matter physics, particle physics, astrophysics, and quantum information processing.

Students will receive an introductory concepts-based approach to the physics of special relativity, nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass, binding energy and nuclear decay. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles and their interactions.

Students will gain an understanding of the basis of Einstein’s theory of special relativity in electro-magnetism, both conceptually and mathematically, and why the theory has replaced Newton’s concepts of absolute space and time. Additionally, students will develop a broad understanding of the equivalence principle and its relevance for general relativity.

Introducing programming basics, this module engages students with the writing and running of computer programs in Python for numerical simulation and data analysis. This will involve learning about variable types, flow control and logical expressions, functions, and classes. They will gain knowledge of software libraries for numerical computations, including the handling of array data formats. They will be introduced to good coding practices, such as documenting and testing their code, and become familiar with methods to debug their programs.

Students will gain the necessary knowledge to model simple physical systems using appropriate programming techniques, and will develop an understanding of numerical precision and accuracy. By learning Object Orientated programming, students will use objects and methods to represent physical systems in order to independently complete an open-ended project to model a physics-based problem.

The module covers the structure and evolution of the Universe from the modern perspective, examining its size and structure, galaxies and galaxy clusters, dark matter and cosmic length and mass scales. Students will learn methods of measuring astronomical and cosmological distances and Hubble-Lemaitre's Law of expansion.

Students will additionally learn the equations that describe the dynamics and evolution of the Universe as well as encounter topics such as dark energy and cosmic inflation, which takes place in the very early Universe, near the Big Bang, through a mixture of lectures and seminars. Finally, the module will discuss the Universe's ultimate fate.

This module provides a review of thermodynamic equilibrium, temperature, zeroth law, reversible and irreversible processes, as well as heat, work and internal energy. Students will be introduced to the Boltzmann distribution and apply the Boltzmann distribution to solids, paramagnetism, heat capacity, defects in solids. The module offers students the opportunity to explore crystal structure and symmetry, lattices, symmetry operations and unit cells. Students will investigate the quantum mechanical free electron model and basic band structure ideas in nearly free electron and tight binding pictures as part of the module.

Students will develop an appreciation for the connections between the microscopic and macroscopic pictures of the thermal properties of solids, and will gain the skillset required to account for some fundamental properties of solids in statistical terms. Additionally, students will become familiar with the use of thermodynamic potentials and associated thermodynamic relations, and will gain an awareness of the different kinds of phase transition and how they are classified. Finally, students will gain the necessary knowledge required to understand the evidence for the third law of thermodynamics and how it relates to the unattainability of absolute zero.

This module introduces one-electron atoms and the spin-orbit magnetic interaction, along with identical particles and the Helium atom. Students will investigate the Fermi gas model and the single particle shell model, and will compare predictions of the shell model for nuclear spins, parities and magnetic moments with experimental results. The module explores the nuclear beta decay process and the Fermi and Gamow - Teller selection rules, and students are provided with a description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.

Students will develop their knowledge in atomic and nuclear physics to an advanced level, and will be able to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure, in addition to gaining the ability to describe the processes of atomic transitions and nuclear decays. The module will provide an explanation of the concept and importance of the parity of an atomic or nuclear state, and will provide students with the opportunity to study the nuclear beta decay process and in particular the neutrino and parity non-conservation.

Students will be examined on material in core physics modules from year one, two and three. There will be a series of workshops prior to the final examination, for discussion about the types of question set on the examination paper and the revision of problem solving and modelling techniques.

The module examines basic physics principles by applying them in situations that use ideas from multiple core physics modules. This module will allow students to demonstrate a broad grasp of physics principles. Ultimately, they will be well practised in the application of physics methodology and general problem solving techniques to a wide range of problems.

The module is compulsory on the Particle Physics, Particle Physics with Cosmology and Theoretical Physics Pathways and an option on all others.

The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles.

By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

The module explores symmetries, the Quark model and gives an introduction to QCD. Students will explore leptons, as well as forces and their carrier particles and Feynman diagrams. The module aims to provide a general introduction to theoretical and experimental topics in elementary particle physics, essentially the Standard Model of particle physics.

Students will gain the ability to describe the main features of the Standard Model of particle physics and understand its place in physics as a whole, and will be able to identify major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used, such as accelerators and detectors. In addition, students will understand the role of symmetry and conservation laws in fundamental physics, and will develop the ability to perform calculations of physically observable quantities relevant to the subject, along with solving problems based on the application of the general principles of particle physics.

The module offers an introduction to electronic, thermal, optical and magnetic properties of solids.

Students will be introduced to theoretical and experimental topics in solid state physics at an advanced level, and will develop an understanding of the main features of the physics of electrons in solids, crystal lattices and phonons, reciprocal lattice and diffraction of waves, the electronic band structure in metals, insulators and semiconductors. Students will explore electronic properties of semiconductors, including the physics of p-n junctions and their optical properties. Students will be introduced to the basics of magnetism in solids.

Students will gain an enhanced understanding of solid state physics, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.

This module explores the ideas, techniques and results of statistical physics. Students will examine gases and the density of states, along with the statistics of gases, fermions and bosons and the two distributions for gases. Maxwell-Boltzmann gases, velocity distribution and fermi-Dirac gases are investigated as the module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics.

Students will provide a unified survey of the statistical physics of gases, including a full treatment of quantum statistics, gaining a fuller insight into the meaning of entropy. Students will gain knowledge in applications of statistics to various types of gas. Ultimately, students will develop the ability to apply expressions and distributions in order to form accurate deductions, for example using the Boltzmann distribution for the probability of finding a system in a particular quantum state. Additionally, students will learn the role of statistical concepts in understanding macroscopic systems, and will be able to describe superfluidity in liquid helium, Bose-Einstein condensation and black body radiation.

The Theoretical Physics Group project is linked to all of our Theory degrees.

In the Theoretical Physics Group Project, students will work as part of a team to undertake an open-ended investigation of a Theoretical Physics-based problem. The project is not tightly-restrained by defined limits, and students have to make decisions about the direction of their research. Recent project areas include machine learning, quantum computing, chaos, and the use of cellular automata to model the spread of disease or forest fires. Students will receive guidance on project management, planning and meetings, and the module will culminate in the submission of a group written report and an individual talk at the physics student conference, The PLACE. The module equips students with the ability to develop a theoretical physics research project with literature searches, formulation, modelling, analysis and presentation.

This module requires students to undertake an independent study in various aspects of theoretical physics. It provides an opportunity for students to extend their preliminary studies by undertaking open-ended investigations into various aspects/problems of theoretical physics. Students will write up their findings in a report.

This module aims to teach analytical recipes of theoretical physics used in quantum mechanics, with the focus on the variational functions method, operator techniques with applications in perturbation theory methods and coherent states of a quantum harmonic oscillator. Students will be trained in the use of the operator algebra of 'creation' and 'annihilation' operators in the harmonic oscillator problem, which will develop a basis for the introduction of second quantisation in many-body systems. In addition, the module will introduce the algebra of creation and annihilation operators for Bose and Fermi systems, along with second-quantised representation of Hamiltonians of interacting many-body systems. Students will learn to apply a mathematical basis of complex analysis in order to solve problems in mathematical and theoretical physics.

Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Python, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.

Students will develop a more thorough knowledge of the Python language, including the use of inheritance, and will be able to write a physics modelling program in Python.

The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative small-scale energy sources.

By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

The module is compulsory in the Astrophysics, Astrophysics with Cosmology and Astrophysics with Space Pathways.

This module provides students with a modern perspective on the Universe, including its size, structure and evolution over roughly 14 billion years. Students will be introduced to orbits, Kepler’s laws, electromagnetic radiation, telescopes and detectors and learn all the major key astronomical tools that allow us to explore the Universe from the smallest to the largest scales.

Once all the physical tools are introduced, the module explores what we know about stars, their formation and evolution, our solar system, and extra-solar planets. It then moves out to our Galaxy and our local group, and travels back in time to explore the Universe and the major events over the last 13 billion years, including with computer simulations.

This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing.

By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers. Students will understand the many uses of lasers in industry, medicine and the environment.

Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.

Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the two-fluid model of plasmas.

Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of Navier-Stokes equations, along with the wider applications of the Navier-Stokes theory to bio-, geo- and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an information-processing system and the interactions between cardiovascular oscillations and brain waves.

Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.

Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then apply their knowledge of physics and mathematics to the understanding of basic principles of living systems – starting from a cell to the cardiovascular system and the brain.

The module is compulsory on the Particle Physics and Particle Physics with Cosmology Pathways and an option on all others.

This module covers various topics, including the CKM matrix and its parameterisations, unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current heavy flavour particle physics topics, such as c- and b-hadron production and decay analysis, along with top quark physics.

Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector and neutrino oscillations, and they will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours, which are likely directions of the experimental particle physics research in Lancaster.

The module consolidates the theoretical concepts of quantum information processing, exploring Dirac notation, density matrices and evolution, and entanglement. Students will also explore qubits, quantum algorithms, circuit design and error connection. In addition, the module will address trapped ions and atoms, Josephson junctions and quantum optics.

By the end of the module, students will be familiar with the fundamental concepts of quantum processing, such as density matrices and the dynamics of quantum systems, and will be able to understand how these can be implemented in realistic devices. Students will learn about experimental implementation based on atom-optical realisations and realisations in the solid state, and will apply these to explore theoretical concepts that have a vast area of application in condensed matter physics and atom-quantum-optics.

This module is compulsory in the Quantum Pathway, and is an option on the other pathways.

This module will provide students with an overview of solid-state realisations of quantum technologies, including superconductivity, low-dimensional structures, and impurity and donor systems, and introduces students to fabrication and characterisation techniques for micro-structures and nano-structures.

Students will develop skills to formulate problems in precise terms, while identifying key issues, to solve problems and provide well-defined solutions. Students will also understand how to collate and understand complex information from a range of sources, including verbal information from lectures, lecture notes, and key textbooks.

The module is compulsory on the Astrophysics with Space Pathway and an option on all other Pathways.

Space and Auroral Physics explores the physics of the solar-terrestrial environment, from the solar wind, which streams from the Sun towards Earth, to how the atmosphere couples to the local space environment. This module will introduce you to basic plasma physics, the dynamics of Earth’s magnetosphere, and the formation of the aurora. It will also address the causes and impacts of space weather of technology and society.

This module is intended to provide students with hands-on experience in delivering scientific outreach and engagement. Students will first attend a series of online introductory lectures to cover the basics of education and engagement, including presenting science to a general audience and inspiring school pupils in STEM. During the second part of this module, students will then prepare and deliver either a taught lesson within a school, a school’s outreach activity (delivered either on campus or in the classroom), or a public engagement activity (such as writing a blog, making a video, or delivering a public lecture). Students will collect evaluation data, and then spend the final week of the course critically reflecting and evaluating the activity they produced.

For certain options, which involve working with young people, it will be necessary to have a DBS check. This will be arranged by the Faculty.

The module is compulsory on the Particle Physics with Cosmology and Astrophysics with Cosmology Pathways and an option on all others.

The module follows the global dynamics of the Universe, the Friedmann equation, energy conservation and acceleration equations. Students will examine the early Universe, the initial singularity and the radiation era of the Hot Big Bang. The thermal history of the Hot Big Bang cosmology is studied as part of the module, along with the formation of large-scale structure (galactic clusters and super-clusters) in the Universe. Students will develop awareness of our current understanding of the observed Universe and the early Universe, and will be able to write down some of the equations that encode this understanding.