Astrophysics MPhys

The module provides an overview of Newtonian mechanics, continuing on from A-level courses. This includes: Newton’s laws of motion in linear and rotational circumstances, gravitation and Kepler’s laws of planetary motion. The theory of Relativity is then introduced, starting from a historical context, through Einstein’s postulates, leading to the Lorentz transformations.

Einstein said in 1949 that "Thermodynamics is the only physical theory of universal content which I am convinced, within the areas of applicability of its basic concepts, will never be overthrown." In this module, different aspects of thermal physics are addressed: (i) classical thermodynamics which deals with macroscopic properties, such as pressure, volume and temperature – the underlying microscopic physics is not included; (ii) kinetic theory of gases describes the properties of gases in terms of probability distributions associated with the motions of individual molecules; and (iii) statistical mechanics which starts from a microscopic description and then employs statistical methods to derive macroscopic properties. The laws of thermodynamics are introduced and applied.

Electricity, Magnetism and Waves lie at the heart of physics, being phenomena associated with almost every branch of physics including quantum physics, nuclear physics, condensed matter physics and accelerator physics, as well as numerous applied aspects of physics such as communications science. The course is roughly divided into two sections. The first part introduces the fundamental concepts and principles of electricity and magnetism at an elementary level and develops the integral form of Maxwell’s equations. The second part involves the study of oscillations and waves and focuses on solutions of the wave equation, the principles of superposition, and examples of wave phenomena.

This module illustrates how a series of fascinating experiments, some of which physics students will carry out in their laboratory courses, led to the realisation that Newtonian mechanics does not provide an accurate description of physical reality. As is described in the module, this failure was first seen in interactions at the atomic scale and was first seen in experiments involving atoms and electrons. The module shows how Newton’s ideas were replaced by Quantum mechanics, which has been critical to explaining phenomena ranging from the photo-electric effect to the fluctuations in the energy of the Cosmic Microwave Background. The module also explains how this revolution in physicist’s thinking paved the way for developments such as the laser.

​ The "Introduction to computational physics" (Phys105) module is designed to introduce physics students to the use of computational techniques appropriate to the solution of physical problems. No previous computing experience is assumed. During the course of the module, students are guided through a series of structured exercises which introduce them to the Python programming language and help them acquire a range of skills including: algorithm development; Manipulating and plotting data in a variety of ways; simple Monte Carlo techniques. The exercises are based around the content of the first year physics modules, both encouraging students to recognise the relevance of computing to their physics studies and enabling them to develop a deeper understanding of aspects of their first year course.  

​This module teaches the laboratory side of physics to complement the taught material from lectures and to introduce key concepts of experimental physics.

​This module aims to provide all students with a common foundation in mathematics, necessary for studying the physical sciences and maths courses in later semesters. All topics will begin "from the ground up" by revising ideas which may be familiar from A-level before building on these concepts. In particular, the basic principles of differentiation and integration will be practised, before extending to functions of more than one variable. Basic matrix manipulation will be covered as well as vector algebra and an understanding of eigenvectors and eigenvalues.

This module introduces some of the mathematical techniques used in physics. For example, differential equations, PDE’s, integral vector calculus and series are discussed. The ideas are first presented in lectures and then the put into practice in problems classes, with support from demonstrators and the module lecturer. When you have finished this module, you should: Be familiar with methods for solving first and second order differential equations in one variable. Be familiar with methods for solving partial differential equations and applications. Have a basic knowledge of integral vector calculus. Have a basic understanding of Fourier series and transforms.

Astronomy is the study of Universe – applying a broad range of physics (and indeed chemistry and even biology) to both understand the cosmos and our place in it, andit and improve our understanding of the underlying physics. In this module you will be introduced to the constituents of the Uuniverse – from our Solar System, through stars, exoplanets and galaxies, to the evolution of spacetime -– and study some of the observational techniques used to answer outstanding questions about the cosmos.

Condensed matter physics (CMP) is the study of the structure and behaviour of matter that makes up most of the things that surround us in our daily lives, including the screen on which you are reading this material. It is not the study of the very small (particle and nuclear physics) or the very large (astrophysics and cosmology) but of the things in between. CMP is concerned with the “condensed” phases of real materials that arise from electromagnetic forces between the constituent atoms, and at its heart is the necessity to understand the behaviour of these phases by using physical laws that include quantum mechanics, electromagnetism and statistical mechanics. Understanding such behaviour leads to the design of novel materials for advanced technological devices that address the challenges that face modern civilization, such as climate change.

​ The study of classical electromagnetism, one of the fundamental physical theories. Several simple and idealised systems will be studied in detail, developing an understanding of the principles underpinning several applications, and setting the foundations for the understanding of more complex systems. Mathematical methods shall be developed and exercised for the study of physical systems.

This module extends the previous treatment of vector calculus and linear algebra (vectors and matrices). It provides essential mathematical tools for electrodynamics and quantum mechanics.

This module introduces the basic properties of particles and nuclei, their stability, modes of decay, reactions and conservation laws. Recent research in particle physics is highlighted, and for nuclear physics some of the applications (such as nuclear power) are given. This module leads on to more specialist optional modules in Year 3, in particle physics, nuclear physics and nuclear power.

​ The course aims to introduce 2nd year students to the concepts and formalism of quantum mechanics. The Schrodinger equation is used to describe the physics of quantum systems in bound states (infinite and finite well potentials, harmonic oscillator, hydrogen atoms, multi-electron atoms) or scattering (potential steps and barriers). Basis of atomic spectroscopy are also introduced. ​

An introduction to basic mathematic concepts and techniques. Following three semester math courses there the emphasis is on solutions of ordinary and partial differential equations with bits also on relativity, statistics and group theory

Why are some stars faint, while others are millions of times brighter than the Sun? Why do some stars appear blue, while others appear red? Why do some stars suddenly explode, while others slowly fizzle out on timescales longer than the age of the Universe? These questions can be answered once we understand the theory of the physics of stellar structure, and how stars of different masses change in appearance as they evolve.

Teaches and explores the fundamental aspects of Practical Optical Astronomy. Predominantly lab based, the module includes a full primer on how to plan and carry out telescopic observations, photometric and spectroscopic techniques, and the analysis of the resultant data.

The problem to understand blackbody radiation opened the door to modern physics. In this module an understanding of thermodynamics is developed from a quantum mechanical and statistical description of the three fundamental gases: The Maxwell-Boltzmann ideal gas in the classical limit, and the Fermi-Dirac and Bose-Einstein gases in the quantum limits for fermions and bosons, respectively. A statistical understanding of thermodynamic quantities will be developed together with a method of deriving thermodynamic potentials from the properties of the quantum system. Applications are shown in solid state physics and the Planck blackbody radiation spectrum.

​The course covers the concepts required to connect special relativity, Newtonian gravity, general relativity, and the cosmological metrics and dynamical equations. The main part of the course is focussed on cosmology, which is study of the content of the universe, structure on the largest scales, and its dynamical evolution. This is covered from both a theoretical and observational perspective. 

The module builds on first and second year modules on electricity, magnetism and waves to show how a wide variety of physical phenomena can be explained in terms of the properties of electromagnetic radiation. The module will also explore how these properties follow from the relationships between electric and magnetic fields (and their interactions with matter) expressed by Maxwell’s equations, and how electromagnetism fits into the theory of Special Relativity.​

​Introduction to Particle Physics.  To build on the second year module involving Nuclear and Particle Physics.  To develop an understanding of the modern view of particles, of their interactions and the Standard Model.

This module gives an introduction to nuclear physics. Starting from the bulk properties of atomic nuclei different modes of radioactivity are discussed, before a closer look at the nucleon-nucleon interaction leads to the development of the shell model. Collective models of the nucleus leading to a quantitative understanding of rotational and vibrational excitations are developed. Finally, electromagnetic decays between excited states are introduced as spectroscopic tools to probe and understand nuclear structure.

​This module concerns the study of quantum mechanics and its application to atomic systems. The description of simple systems will be covered before extending to real systems. Perturbation theory will be used to determine the detailed physical effects seen in atomic systems.

​This module covers the physics and observational techniques of the field of Galactic Astrophysics

​This module provides a detailed overview of the practicalities of observational astronomy across the entire electromagnetic spectrum.

Condensed Matter Physics (CMP) is the largest subfield of physics with practical applications that has changed our everyday life such as semiconductor devices, magnetic recording disks, Magnetic resonance imaging. It deals with the study of the structure and physical properties of large collection of atoms that compose materials, which are found in nature or synthesized in laboratory. This particular module aims to advance and extend the concepts on solids introduced in Year 1 and Year 2 modules. Especially, it focuses on the atomic structure and behaviour of electrons in crystalline materials, which are essential for understanding of physical phenomena in complex systems.

Preparation and characterisation of a range of materials of scientific and technological importance.

This course considers the application of physics to the study of planets, with a focus on the application of fundamental physical principles rather than providing detailed planetary descriptions. The first four weeks address the planets of our solar system, including what constraint is provided on their physics from studies of our own planet, Earth. We consider particularly insights from observations of orbits, gravitational field, rotation, thermal properties and magnetic field, with brief coverage of formation,composition, and seismology. The focus is on application of basic physical principles rather than detailed observational descriptions, and on methods that might (eventually) be of use in the study of exoplanets. The final two weeks considers exoplanets specifically, particularly the methods of their detection,and our current understanding of planetary systems in general.

This module develops the physics concepts describing semiconductors in sufficient details for the purpose of understanding the construction and operation of common semiconductor devices.

​This c ourse aims at providing students with a basic knowledge of the principles of radiation transport, the interaction of photons and matter, the computation of stellar atmosphere models, the application of radiation transport methods to expanding atmospheres such as stellar winds and Supernova envelopes. We also look at how stellar winds are created and at the properties of Supernovae. ​

​ This module gives a brief introduction into the physics of solid surfaces their experimental study. Surfaces and interfaces are everywhere and many surface-related phenomena are common in daily life (texture, friction, surface-tension, corrosion, heterogeneous catalysis). Here we are concerned with understanding the microscopic properties of surfaces, asking questions like: what is the atomic structure of the surface compared to that of the bulk? What happens to the electronic properties and vibrational properties upon creating a surface? What happens in detail when we adsorb an atom or a molecule on a surface? This module will mostly concentrate on simple model systems like the clean and defect-free surface of a single-crystal substrate.

In this module, students will develop an understanding of the principles of radiotherapy and treatment planning. Topics include interaction of radiation with biological matter, radiation transport, biological modelling, beam modelling, medical imaging, electron transport and treatment planning.

Einstein’s theories of special and general relativity have introduced a new concept of space and time, which underlies modern particle physics, astrophysics and cosmology. It makes use of, and has stimulated the development of modern differential geometry. This module develops the required mathematics (tensors, differential geometry) together with applications of the theory to particle physics, black holes and cosmology. It is an essential part of a programme in theoretical physics.

​Statistical Methods in Physics Analysis: Understanding Statistics and its application to data analysis

​This module involves the student engaging in a detailed project typically based in one of the research groups within the Department of Physics. The student will be conducting independent research under the supervision of one or more academic staff members. The output of the project will be written up in a project report and presented in the form of a poster.

​This module will cover the physics of the interstellar medium (ISM) — the gas in between stars. Students will learn how observations, specifically spectroscopy, allows astronomers to understand the physical conditions and chemical content of the ISM and thereby construct models of the ISM and its relationship to the formation and evolution of stars and galaxies.  The module is taught by directed reading and problem-solving. Students are expected to read a  section of a textbook and attempt a set of problems every week, and the content and problems will be reviewed at  weekly tutorial sessions. ​

The Astrophysics Field Trip to the Teide Observatory, Tenerife, Canary Islands. One week trip where students will employ at least the Mons and Liverpool Telescopes (plus others if available) to plan, carry out, and analyse astronomical observations.

There are almost 50,000 particle accelerators in the world, ranging from the linear accelerators used for cancer therapy in modern hospitals to the giant ‘atom-smashers’ at international particle physics laboratories used to unlock the secrets of creation.

Accelerator and beam physics is a broad discipline that draws on concepts from linear and nonlinear mechanics, electrodynamics, special relativity, plasma physics, statistical mechanics, and quantum mechanics.

This course covers the fundamental physical principles of particle accelerators, with a focus on basic beam dynamics and beam diagnostics. It teaches the fundamental concepts of the most commonly used accelerator types, beam motion and diagnostics. The course links these concepts to the current research programmes of the Liverpool Accelerator Group, based at the Cockcroft Institute.

​ The Advanced Nuclear Physics course introduces forms of the nucleon-nucleon interaction and the nuclear mean-field potential. Deformation (non-spherical nuclear shapes) is introduced via the deformed shell model (Nilsson model) and collective modes of excitation discussed. Exotic nuclear behaviour at the extremes of spin (angular momentum), isospin (proton-neutron imbalance) and charge/mass (superheavy elements) is presented. Various types of nuclear reaction are discussed, particularly in relation to the astrophysical creation of the elements.​

This module looks at how basic calculations are done in particle physics.
Relativistic quantum mechanics and their limitations are introduced and applied to various particle physics problems. Feynman rules are discussed and examples of calculations of cross sections and particle lifetimes are given in the context of electromagnetic, weak and strong interactions. The development of the electroweak theory and the Higgs boson, as well some historical elements and description of current particle physics research are also covered.

Modern concepts and advanced quantum mechanics problems will be discussed in depth and supported by complex calculations. In the course it will be demonstrated that quantum mechanics is an extraordinary successful theory describing nature, i.e. part of the course emphasis is on applications of quantum physics and state-of-the art experiments, but not always in full detail​.

The module will build on students’ existing knowledge of Newtonian mechanics, and introduce important principles, concepts and techniques from Lagrangian and Hamiltonian mechanics.   The core material will be based on systems of particles, but field theory will also be discussed.   The focus will be on application of these topics to classical systems, but this will also give some insight into fundamental aspects of modern physics (including quantum mechanics).   Delivery will be through lectures and tutorials/problems classes.

​ Stellar clusters, galaxies, clusters of galaxies are held together by mutual gravity of their components: mainly stars and possibly dark matter. In this module, you will learn how systems containing millions and billions of point-like gravitating bodies sustain and evolve. Although only Newton’s law shapes these systems, you will see that a lot can be implied from it when one employs sophisticated mathematical tools.​

This module introduces the current and active field of nanoscale physics and technology. It will cover basic physics at the nanoscale as well as nanoscale fabrication and characterisation techniques and will discuss a range of applications of nanostructures.

This module will look at some of the many ways that matter and radiation interact, in relativistic and non-relativistic physical contexts. The aims of the module are:

To see how physical phenomena can be applied and used to explain the appearance and spectra of celestial objects
To provide an astrophysical context for statistical mechanics
To introduce Einstein’s A and B coefficients
To understand the importance of the hydrogen 21cm line
To demonstrate how emission line ratios inform on physical properties​.

This module starts from our knowledge of stellar evolution, to describe methods employed by astrophysicists to determine chemical composition and ages of stellar populations in the universe. This is a crucial information needed to understand how galaxies form and evolve in time. Examples of applications of these techniques to real observations will be also shown.​

Building on the content of the Stellar Atmospheres Module, Time Domain Astrophysics explores the transient Universe, in particular the explorive transients such as Novae, Supernovae, and Gamma Ray Bursts. This module is delivered by an ensemble of staff, all delivering content in which they are expert researchers.