Physics - MPhys

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This module provides an introduction to quantum mechanics, developing knowledge of wave-functions, the Schrodinger equation, solutions and quantum numbers for important physical properties. Topics include: 2-state systems. Bras and kets. Eigenstates and Eigenvalues; Superposition Principle; Probability Amplitudes; Change of Basis; Operators. The Schrodinger equation. Stationary states. Completeness. Expectation values. Collapse of the wave function. Probability density. Solutions of the Schrodinger equation for simple physical systems with constant potentials: Free particles. Particles in a box. Classically allowed and forbidden regions. Reflection and transmission of particles incident onto a potential barrier. Probability flux. Tunnelling of particles. The simple harmonic oscillator. Atomic vibrations.

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This module will build on the general principles of quantum mechanics introduced earlier in the degree and applied them to the description of atoms, starting by the description of the hydrogen atom and covering other topics such as the effect of magnetic fields on an atom or X-ray spectra.

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This module looks to introduce a range of important laws and principles relating to the physics of electromagnetism and optics. Students will also learn mathematical techniques to enable the modelling of physical behaviour and apply important theory to a range of electromagnetism and optics scenarios.

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In this module students develop their experience of the practical nature of physics, including developing their ability to execute an experiment, and to use programming scripts to process data. Students also develop their skill in analysis of uncertainties, and comparison with theory. The module strengthens students' communication skills and knowledge of, and ability to write, all components of laboratory reports.

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This module introduces and develops a knowledge of numerical approximations to solve problems in physics, building on the programming skills gained in earlier stages. In addition, it complements the analytical methods students are trained to use and extends the range of tools that they can use in later stages of the degree. This module covers for example how to solve linear equations, how to find eigenvalues and numerical integration and differentiation.

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The module will provide a firm grounding in mathematical methods: both for solving differential equations and, through the study of special functions and asymptotic analysis, to determine the properties of solutions.

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This module builds on the brief introduction to astronomy previously taught in earlier stages. Students enhance their knowledge of astrophysics through the study of the theory, formalism and fundamental principles developing a rigorous grounding in observational, computational and theoretical aspects of astrophysics. In particular they study topics such as properties of galaxies and stars and the detection of planets outside the solar system.

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This module aims to provide a basic understanding of the major subsystems of a spacecraft system and the frameworks for understanding spacecraft trajectory and orbits, including interplanetary orbits, launch phase and altitude control. Students will also gain an awareness of ideas on how space is a business/commercial opportunity and some of the management tools required in business.

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After taking the classes students should be more fluent and adept at solving and discussing general problems in Physics (and its related disciplines of mathematics and engineering).

There is no formal curriculum for this course, which uses and demands only physical and mathematical concepts with which the students at this level are already familiar.

Problems are presented and solutions discussed in topics spanning several topics in the undergraduate physics curriculum (Mechanics and statics, thermodynamics, and optics, etc).

Problems are also discussed that primarily involve the application of formal logic and reasoning, simple probability, statistics, estimation and linear mathematics.

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Special Relativity: Limits of Newtonian Mechanics, Inertial frames of reference, the Galilean and Lorentz transformations, time dilation and length contraction, invariant quantities under Lorentz transformation, energy momentum 4-vector.

Maxwell's equations: operators of vector calculus, Gauss law of electrostatics and magnetostatics, Faraday's law and Ampere's law, physical meanings and integral and differential forms, dielectrics, the wave equation and solutions, Poynting vector, the Fresnel relations, transmission and reflection at dielectric boundaries.

Modern Optics: Resonant cavities and the laser, optical modes, Polarisation and Jones vector formulation.

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Thermodynamics

Review of zeroth, first, second laws. Quasistatic processes. Functions of state. Extensive and intensive properties. Exact and inexact differentials. Concept of entropy. Heat capacities. Thermodynamic potentials: internal energy, enthalpy, Helmholtz and Gibbs functions. The Maxwell relations. Concept of chemical potential. Applications to simple systems. Joule free expansion. Joule-Kelvin effect. Equilibrium conditions. Phase equilibria, Clausius-Clapeyron equation. The third law of thermodynamics and its consequences – inaccessibility of the absolute zero.

Statistical Concepts and Statistical Basis of Thermodynamics

Basic statistical concepts. Microscopic and macroscopic descriptions of thermodynamic systems. Statistical basis of Thermodynamics. Boltzmann entropy formula. Temperature and pressure. Statistical properties of molecules in a gas. Basic concepts of probability and probability distributions. Counting the number of ways to place objects in boxes. Distinguishable and indistinguishable objects. Stirling approximation(s). Schottkly defect, Spin 1/2 systems. System of harmonic oscillators. Gibbsian Ensembles. Canonical Ensemble. Gibbs entropy formula. Boltzmann distribution. Partition function. Semi-classical approach. Partition function of a single particle. Partition function of N non-interacting particles. Helmholtz free energy. Pauli paramagnetism. Semi Classical Perfect Gas. Equation of state. Entropy of a monatomic gas, Sackur-Tetrode equation. Density of states. Maxwell velocity distribution. Equipartition of Energy. Heat capacities. Grand Canonical Ensemble.

Quantum Statistics

Classical and Quantum Counting of Microstates. Average occupation numbers: Fermi Dirac and Bose Einstein statistics. The Classical Limit. Black Body radiation and perfect photon gas. Planck's law. Einstein theory of solids. Debye theory of solids.

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To provide an introduction to solid state physics. To provide foundations for the further study of materials and condensed matter, and details of solid state electronic and opto-electronic devices.

Structure:

Interaction potential for atoms and ions. Definitions, crystal types. Miller indices. Reciprocal lattice. Diffraction methods.

Dynamics of Vibrations.

Lattice dynamics, phonon dispersion curves, experimental techniques.

Electrons in k-space: metals.

Free electron theory of metals. Density of states. Fermi-Dirac distribution. Band theory of solids - Bloch's theorem. Distinction between metals and insulators. Electrical conductivity according to classical and quantum theory. Hall effect.

Semiconductors.

Band structure of ideal semiconductor. Density of states and electronic/hole densities in conduction/valence band. Intrinsic carrier density. Doped semiconductors.

Magnetism.

Definitions of dia, para, ferromagnetism. Magnetic moments. General treatment of paramagnetism, Curie's law. Introduction to ferromagnetism.

Find out more about PHYS6060

This module provides a foundation in numerical approximations to analytical methods – these techniques are essential for solving problems by computer. An indicative list of methods is: Linear equations, zeros and roots, least squares & linear regression, eigenvalues and eigenvectors, errors and finite differences, linear programming, interpolation and plotting functions, numerical integration, numerical differentiation, solutions to ordinary differential equations using numerical methods.

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This module will introduce students to basic concepts in nuclear and particle physics, and will provide an understanding of how the principles of quantum mechanics are used to describe matter at sub-atomic length scales. The following concepts will be covered:

* Properties of nuclei: Rutherford scattering. Size, mass and binding energy, stability, spin and parity.

* Nuclear Forces: properties of the deuteron, magnetic dipole moment, spin-dependent forces.

* Nuclear Models: Semi-empirical mass formula M(A, Z), stability, binding energy B(A, Z)/A. Shell model, magic numbers, spin-orbit interaction, shell closure effects.

* Alpha and Beta decay: Energetics and stability, the positron, neutrino and anti-neutrino.

* Nuclear Reactions: Q-value. Fission and fusion reactions, chain reactions and nuclear reactors, nuclear weapons, solar energy and the helium cycle.

* Experimental methods in Nuclear and Particle Physics (Accelerators, detectors, analysis methods, case studies will be given).

* Discovery of elementary particles and the standard model of particles

* Leptons, quarks and vector bosons

* The concept of four different forces and fields in classical and quantum physics; mediation of forces via virtual particles, Feynman Diagrams

* Relativistic Kinematics

* Relativistic Quantum Mechanics and Prediction of Antiparticles

* Symmetries and Conservation Laws

* Hadron flavours, isospin, strangeness and the quark model

* Weak Interactions, W and Z bosons

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Students will develop a number of skills related to the investigation and planning of research such as analytical skills, critical thinking and ability to understand and communicate scientific information in graphically. Students will learn how to search and retrieve information from a variety of locations (colloquia, websites, journals, proceedings etc). They will learn how to compile professionally-produced scientific documents such as colloquia reports, posters and applications for funding of future research activities/research job applications. The Group research investigation strengthens these skills, adding experience of working in a team.

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Aims:

To provide an experience of open-ended research work.

To begin to prepare students for postgraduate work towards degrees by research or for careers in R&D in industrial or government/national laboratories.

To deepen knowledge in a specialised field and be able to communicate that knowledge orally and in writing.

Syllabus

All MPhys students undertake a laboratory, theoretical or computationally-based project related to their degree specialism. These projects may also be undertaken by Diploma students. A list of available project areas is made available during Stage 3, but may be augmented/revised at any time up to and including Week 1 of Stage 4. As far as possible, projects will be assigned on the basis of students' preferences – but this is not always possible: however, the project abstracts are regarded as 'flexible' in the sense that significant modification is possible (subject only to mutual consent between student and supervisor). The projects involve a combination of some or all of: literature search and critique, laboratory work, theoretical work, computational physics and data reduction/analysis. The majority of the projects are directly related to the research conducted in the department and are undertaken within the various SPS research teams.

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Introduction. Magnetism, magnetometry and measuring techniques, Localised magnetic moments, spin and orbital moments, magnetic moments in solids. Paramagnetism. Exchange interactions, direct, indirect and superexchange, Magnetic structures, ferro, ferri, antiferromagnetism. Neutron and X-ray scattering. Spin waves, magnons. Magnetic phase transitions. Superconductivity: Introduction to properties of superconductors, Thermodynamics and electrodynamics of superconductors, Type I and Type II superconductors, the flux lattice Superconducting phase transitions. Microscopic superconductivity, correlations lengths, isotope effect, Cooper pairs, Froehlich Interaction, BCS theory. High Tc superconductors, superfluids, liquid helium.

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Quantum mechanics is the theoretical basis of much of modern physics. Building on the introductory quantum theory studied in earlier stages, this module will review some key foundational ideas before developing more advanced topics of quantum mechanics and quantum field theory.

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In this module you learn what is meant by neural networks and how to explain the mathematical equations that underlie them. You also familiarise yourself with cognitive neural networks using state of the art simulation technology and apply these networks to the solution of problems. In addition, the module discusses examples of computation applied to neurobiology and cognitive psychology. The module also introduces artificial neural networks from the machine learning perspective. You will study the existing machine learning implementations of neural networks, and you will also engage in implementation of algorithms and procedures relevant to neural networks.

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This module will give students an overarching introduction to quantum information processing (QIP). At the end of the course the students will have a basic understanding of quantum computation, quantum communication, and quantum cryptography; as well as the implications to other fields such as computation, physics, and cybersecurity.

We will take a multi-disciplinary approach that will encourage and require students to engage in topics outside of their core discipline. The module will cover the most essential mathematical background required to understand QIP. This includes: linear algebra, basic elements of quantum theory (quantum states, evolution of closed quantum systems, Born's rule), and basic theory of computing. The module will introduce students to the following theoretical topics: quantum algorithms, quantum cryptography, quantum communication & information. The module will also address experimental quantum computation & cryptography.

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Space Astronomy:

Why use space telescopes; other platforms for non-ground-based astronomical observatories (sounding rockets, balloons, satellites); mission case study; what wavelengths benefit by being in space; measurements astronomers make in space using UV, x-ray and infra-red, and examples of some recent scientific missions.

Exploration of the Solar System:

Mission types from flybys to sample returns: scientific aims and instrumentation: design requirements for a spacecraft-exploration mission; how to study planetary atmospheres and surfaces: properties of and how to explore minor bodies (e.g. asteroids and comets): current and future missions: mission case study; how space agencies liaise with the scientific community; how to perform calculations related to the orbital transfer of spacecraft.

Solar System Formation and Evolution:

The composition of the Sun and planets will be placed in the context of the current understanding of the evolution of the Solar System. Topics include: Solar system formation and evolution; structure of the solar system; physical and orbital evolution of asteroids.

Extra Solar Planets:

The evidence for extra Solar planets will be presented and reviewed. The implications for the development and evolution of Solar Systems will be discussed.

Life in Space:

Introduction to the issue of what life is, where it may exist in the Solar System and how to look for it.

Find out more about PHYS7090

Flight Operations: Control of spacecraft from the ground, including aspects of telecommunications theory.

Propulsion and attitude control: Physics of combustion in rockets, review of classical mechanics of rotation and its application to spacecraft attitude determination and control.

Impact Damage: The mechanisms by which space vehicles are damaged by high speed impact will be discussed along with protection strategies.

Human spaceflight: A review of human spaceflight programs (past and present). Life-support systems. An introduction to some major topics in space medicine; acceleration, pressurisation, radiation, etc.

International Space Station: Status of this project/mission will be covered.

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Chemists and physicists are now playing an important role in the growing field of materials research. More recently, there has been a growing interest, driven by technological needs, in materials with specific functions and this requires a combination of physics and chemistry. For example, new materials are needed for the optics and electronics industry (glasses and semiconductors). The aim of this module is to introduce students to this area of modern materials and associated techniques. Examples of the topics that might typically be covered are: Crystals and crystallography; Molecular materials; Glasses; Magnetism and Magnetic Materials; Multiferroics; X-ray absorption spectroscopy (XAS).

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