**Electromagnetism, Optics and Lasers**

Electromagnetism forms the basis of wave based optics. The aim of this section of the module is to extend the material covered in Stage 2 to introduce Maxwell’s equations in vector differential point form. From this, the concept of light as an electromagnetic wave will be developed. The main characteristics of such waves will be explored as will their propagation behaviour in various media. The initial section concentrates on the development of the electromagnetic theory needed to explain the plane electromagnetic wave. In the optics section this is applied to some classical topics in optics while the third section extends this to basic laser theory.

**Solid State Physics**

This module in solid state physics examines the mechanical electrical and magnetic properties of solid materials. It explores the origins of such properties developing the theories underpinning experimental observation in metals, semiconductors, polymers and ceramics.

**Quantum Physics**

This section will introduce the concepts of Schrödinger’s approach to quantum mechanics. Measurement operators for observable quantities, such as energy and momentum, will be applied to a range of problems and the solutions analysed.

**Curricular information is subject to change***Electromagnetism (12 lectures)**

Review of laws of electromagnetism,

Description of fields, div, curl and grad,

Stokes and Gauss theorems,

Displacement current.

Expression of the Laws of electromagnetism in vector differential point form: Maxwell’s equations

Poynting vector.

Group and phase velocities.

Propagation of electromagnetic waves in (a) ideal dielectrics, (b) metals: skin depth.

**Optics (6 lectures)**

Plane wave mathematical representation, superposition, irradiance.

Coherence.

Polarisation: analysis of circularly and elliptically polarised light.

Diffraction, Fraunhofer, Fresnel.

Interference: Fabry-Perot and Michelson Interferometers, visibility, resolving power, free spectral range.

Diffraction of circular and single slit apertures, the diffraction grating.

**Lasers (6 lectures)**

Absorption and emission of light.

Population inversion.

Gain and the optical amplifier

Feedback and the optical oscillator

Modes and output frequency.

**Solid State Physics (24 Lectures)**

Review of basic crystallography. Lattice defects. Review of elasticity, stress, strain, Hooke’s law, the elastic moduli, strength, stiffness, and elastic deformation. Dislocations and plasticity, Schmid’s law. Strengthening mechanisms, work hardening, grain boundary hardening. Annealing processes in materials, process of recovery, recrystallisation and grain growth. Mechanical testing. Fracture mechanisms, brittle fracture and ductile fracture. Fatigue

Solid solution and intermediate phases, phonons, equilibrium phase diagrams of multi-phase solids and intermediate phases, eutectic, peritectic, eutectoid, hypo/hyper – euctectoid Free energies of solid state phase transitions.

Spin, magnetism of free atoms, origins of atomic magnetism, spin-orbit interaction, total angular momentum J, transistion rates, solid magnetism, spin paramagnetism, Curie law, ferromagnetism, domains, antiferromagnetism and ferrimagnetism.

Diffraction from crystals – 2D crystal structure, Surface reconstructions, Surface overlayer structures, nomenclature for 2D surfaces, Low energy electron diffraction technique(LEED), reciprocal net in 2D, Diffraction in 3D, Bragg Diffraction, Atomic Scattering Factor, Structure Factor, Laue conditions, Reciprocal lattice, Diffraction techniques, Debye-Scherrer Method.

Electrical Properties of Solids/ Introductory Bandstructure – Drude theory of electrical conductivity in solids, Basic assumptions, DC electrical conductivity, Collisions and relaxation times, Matthiesen’s rule, Hall effect and magnetoresistance, AC electrical conductivity, Dielectric function and plasma resonance, Thermal conductivity, Wiedemann- Franz Law and Lorentz number.

Bloch’s quantum theory of conduction – Electrons in a periodic potential, Energy band structure, Electron statistics.

**Quantum Physics (24 Lectures)**

Review of Classical Mechanics applied to microscopic systems.

Vector Spaces and Matrices. Matrices as operators. Hermitian matrices, operators, eigenvectors and eigenvalues. Dirac Notation. Delta functions. Functions as vectors. Representation and Basis. Inner product.

Basic principles of quantum mechanics. Wavefunctions, operators and observables. The uncertainty principle. Probability. Eigenvalues and expectation values.

Energy operators:

The Time Independent Schrodinger Equation and it justification from de Broglie. Application to simple systems. Normalisation. Expectation Values.

The Time Independent Schrodinger Equation. Superposition states. Orthonormality. Time evolution of a state.

The momentum operator, eigenvalues and expectation values

The position operator.

The Hamiltonian applied to various potential wells in 1, 2 and 3D, such as finite wells, potential steps, potential barriers and linear ramps. Degeneracy. Barrier penetration, tunnelling, transmission and reflection coefficients.

Commutation of operators, conjugate variables and the uncertainty principle.

The harmonic oscillator, its Hamiltonian, energy eigenfunctions and eigenvalues. Creation and annihilation operators. Coherent states.

The gaussian wavepacket and uncertainty.

Angular momentum. Orbital angular momentum, the L_{z} and L^{2} operators, their eigenfunctions and eigenvalues. Spin angular momentum: Pauli matrices, S_{z} and S^{2} operators, eigenvalues. Magnetic moments.

An electron in a central potential: the Hydrogen atom. Radial and tangential functions. Orbitals.

Multi particle wavefunctions, indistinguishability. Fermions and Bosons. Introduction to quantum statistics. The Pauli exclusion principle and the exchange interaction.

Time independent perturbation theory to first order.

Lectures supported by tutorials, problem sheets, discussion and self directed learning.

Module Content & Assessment | |
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Assessment Breakdown |
% |

Formal Examination | 70 |

Other Assessment(s) | 30 |