Second Year
Listed here are descriptions of each course available in the second year of study in the department. Select a link below to view a short summary of the course.
PH2130 - Mathematical Methods
- Ordinary differential equations: physical origins, linear equations with constant coefficients, homogeneous and inhomogeneous equations, exact differentials, integrating factors, simple power series method, sines and cosines, Legendre’s equation and Legendre polynomials, Frobenius method, Bessel’s equation and Bessel functions, Sturm-Liouville theorem and orthogonality, orthogonal expansions, Fourier series and other examples.
- Partial differential equations: physical origins, the Laplacian, separation of variables, boundary conditions, Cartesian coordinates, polar coordinates, circular membrane, spherical coordinates, Legendre’s equation.
- Integral transforms: Fourier transform and its physical meaning, solutions with Fourier transforms.
- Gamma function and Dirac delta function.
PH2150 - Scientific Computing Skills
- Basics of numerical calculation on computers: Types of computing. Numerical, symbolic, procedural, object orientated.
- Arrays and Matrices: Arrays for storing data, manipulating arrays. Using arrays and matrices (Eigenvector, inversion).
- Plotting and visualization: Scatter plots, Histograms, Multi-dimensional plots.Data analysis: Mean/mode/median; Variance, RMS, kertosis, moments; Fitting (least squares); Regression.
- Advanced data analysis: Fourier series, Fourier transform, Smoothing.
- Programming: Control structures (if, for, while, return etc). Functions, program layout
- Simulation: Evaluation of simple and complex expressions. Monte Carlo. Numerical integration.
- Differential equations: Difference methods. Leap-frog method. Runge Kutta.
- Monte Carlo methods: Metropolis algorithm. Integrals, integral estimation
- Linear equations: Solutions, eigenvalues. Diagonalisation. Factorisation.
- Project report: example illustrating physics from 2nd year core.
PH2210 - Quantum Mechanics
Electron diffraction experiments show that the electron, which is classically thought of as a particle, can be equally well described as a wave. In this course we will show that any small particle can be described by wavefunction that obeys Schrodingers equation, a differential equation that like Newton's equation (F=ma) is important in determining in what happens next, that is how the wavefunction evolves with time. Having defined the wavefunction the main purpose of the course is to understand how the electrons in an atom come to be in particular orbits, which determines the atom's chemical and physical properties. This requires an understanding of angular momentum and spin, the latter being a quantum mechanical concept that has not classical analogy.Quantum mechanics is probably the most successful theoretical description of the world as we know it, and its development in the early 20th century involved physics greats such as Schrodinger, Born, Dirac, Bohr, Heisenberg, Pauli, ..
- Review of the failure of classical physics and the introduction of quantum ideas; the uncertainty principle. Schrödinger’s equation; the wave function and its interpretation.
- Operators, eigenvalues, eigenfunctions, expectation values; commutation relations, non-commutation.
- Applications of Schrödinger’s equation in one-dimension: free particle, square well, harmonic oscillator; potential step, barrier and tunnelling (including alpha decay).
- Applications of Schrödinger’s equation in three dimensions: particles in a rectilinear box, angular momentum, the hydrogen atom.
- The exclusion principle, atomic structure and the periodic table. Mixed states. Simple perturbation theory.
PH2310 - Optics
- Definition of Fourier transforms and their properties; Convolution and Transfer functions; Various applications of Fourier Transforms; Solutions of Differential Equations using Fourier Transforms.
- Geometrical optics. Fraunhofer and Fresnel diffraction. Optical instruments: image formation and quality. Rayleigh criterion and resolving power, aberrations. Interference. Two-beam and multiple-beam effects. Interferometers. Thin films.Dispersion in dielectric media. Normal and anomalous dispersion. Scattering of e-m radiation. Polarisation by scattering and other means.
- Masers and lasers: history; spontaneous and stimulated emission; Einstein coefficients; practical details of lasers and laser systems; properties of laser light.Fourier optics and diffraction; Huygens-Fresnel theory of diffraction; Gaussian beams; spatial and temporal coherence; applications to optical imaging, image processing and Fourier Transform spectroscopy.
PH2420 - Electromagnetism
The electromagnetic force is one of the four fundamental forces of nature, and as such pervades all of physics. All of electromagnetism is embodied in Maxwell’s equations, and an understanding of these equations and their consequences is the objective of this course. Studies in electricity and magnetism led ultimately to the prediction and finally the generation and detection of electromagnetic radiation. All this and more is described in this course.
- Vector calculus treatment of Electrostatics: the electric field, Coulomb’s and Gauss’ laws, electric field energy, equations of Poisson and Laplace.
- Steady currents: continuity equation, Kirchhoff’s laws, Laplace’s equation in conductors.
- Vector calculus treatment of the magnetic effects of currents: Biot-Savart law, magnetic field, Ampère’s law, Lorentz force, energy of a magnetic field.
- Induction; Faraday’s law, Lenz’s law. Displacement current.
- Electric and magnetic dipoles and the electromagnetism of matter. Macroscopic fields E, D, B and H; their boundary conditions at interfaces.
- Maxwell’s equations; plane waves in free space and in media; reflection, refraction, polarisation. Poynting vector. The EM spectrum. Radiation pressure.
- Propagation in lossy media: dielectric loss, ohmic loss, skin depth; electromagnetic screening.
- Electromagnetic potentials. Gauge freedom. Scalar and vector potentials for stationary and time varying problems. Radiation from dipoles.
- Incompatibility of Maxwell’s equations and Newton’s laws. Resolution by Lorentz transformation and special relativity.
PH2510 - Atomic and Nuclear Physics
- Single-electron atoms.
- Multi-electron atoms.
- Atomic spectra.
- X-ray spectra.
- Hyperfine structure.
- Experimental techniques.
- Nuclear models.
- Radioactive decay: alpha, beta and gamma decay.
- Nuclear reactions: Fission, fusion, chain reaction.
- Interaction of radiation with matter.
- Nuclear radiation detectors.
PH2520 - Particle Detectors and Accelerators
- Detectors: Interaction of particles in matter, energy loss processes. General characteristics of detectors: sensitivity, resolution, efficiency, dead time. Principles of operation of ionisation, scintillation, semiconductor and Cherenkov detectors. Applications to the tracking, energy measurement and identification of particles in particle physics experiments. Study of al multi-purpose detector in high energy physics, integrating several of the detection methods above.
- Accelerators: Introduction to the basic physical principles underlying the operation of modern accelerators. Transverse motion of particles in a beam; beam optics: bending and focusing elements. Accelerating cavities. Synchrotron radiation. Circular and linear accelerator designs. Methods for measurement of energy, luminosity and polarisation in colliders. Study of the design and the operation of e+e- and hadron colliders. Introduction to some applications in the area of medical physics.
PH2610 - Classical and Statistical Thermodynamics
The first section of the course completes the classical treatment of thermal physics started in the first year course, Classical Matter. The power of this treatment is its generality and the fact that it does not rely on microscopic models. In the second section of the course, a microscopic understanding of thermal physics is developed, building on the kinetic theory treatment of a classical gas introduced in Classical Matter, by the introduction of elementary quantum mechanics. Familiar results will be obtained, for example the thermodynamic properties of an ideal gas will be derived from the solutions of Schrödinger’s equation for particles in a box, and exotic new phenomena are encountered, such as negative temperature, superfluidity and superconductivity. This treatment links in an elegant manner the quantum world with everyday observables of systems containing large numbers of particles.
- Thermodynamic equilibrium and processes. The zeroth and first law of thermodynamics.
- Temperature, heat and work. Properties of ideal gases. Counting microstates, order and entropy. The second law of thermodynamics. The statistical mechanics of localised systems: the spin ½ paramagnet, Einstein model of a solid. Boltzmann distribution, partition function.
- Entropy in thermo-dynamics. Cyclic processes and heat engines. Thermodynamic potentials: equilibrium, Maxwell’s relations and their applications. Statistical mechanics of gases, density of states. Calculation of properties of gases in the classical limit, partition function, entropy, equation of state, Maxwell-Boltzmann velocity distribution. Collisions and transport properties. Fermi gases: the Fermi Dirac distribution function. Application to electrons in metals and liquid 3He. Bose gases: The Bose-Einstein and Planck distribution functions.
- Applications to photons (black body radiation), phonons (Debye model), liquid 4He. Phase equilibrium. Generic phase diagram. Conditions for phase coexistence. Clausius-Clapeyron equation. Applications to real systems, including 3He. The third law of thermodynamics and the unattainability of absolute zero.
PH2710 - The Solid State
- Structure, symmetry and properties of solids.
- Mechanical properties: plastic deformation, dislocations.
- Methods of probing solids. X-ray diffraction.
- Thermal properties of solids, phonons.
- Electrical properties of metals, alloys and semiconductors.
- Quantum theory of solids. Energy bands. Bloch theorem.
- Fermiology.
- Intrinsic and extrinsic semiconductors. p-n junctions. Hall effect.
- Magnetic properties: dia-, para-, ferro- and anti-ferro-magnetism.
PH2900 - Astornomy
- Observing the Universe: Observations in different wavelengths.
- Earth and space-based telescopes (and related instruments) and their merits and limitations.
- Basic parameters and measurements in Astronomy: coordinate systems, timekeeping systems, magnitude, angular size, luminosity, colour, mass, distance, temperature, standard candles, redshift.
- The structure and dynamics of the solar system.
- The contents of the solar system: the planets and their moons, rings, asteroids, comets, dust, the solar wind.
- An introduction to planetary geology.