Particles, Quanta and Fields

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

1. Critically review the essential concepts of quantum mechanics, such as the wave-function, the wave equation, eigenvalue equations, operators, angular momentum and spin, commutation and uncertainty relations, matrix mechanics, perturbation theory.
2. Discuss the application of quantum mechanics to the hydrogen atom and bound states, electron spin.
3. Evaluate the thermodynamic behaviour of many body quantum systems.
4. Justify the form of modern particle physics starting with the Lagrangian formalism and the principles of special relativity.
5. Discuss particle cross-sections, collisions and decays in terms of Feynman diagrams.

This Year 3, 20-credit module continues the development of Quantum Physics treating standard situations of bound states (hydrogen atom), scattering states, and progressing through to an introduction to Elementary Particle Physics.

Quantum Physics: Time-dependent Schrödinger equation, variational principle, perturbation theory, two-particle systems, Spin & Orbital Angular Momentum, Addition of Angular Momentum.

Atomic Physics: the hydrogen atom, spherical harmonics.

Relativistic Kinematics: Lorentz and Poincaré transformations, 4-vectors, Covariance, Energy & momentum conservation, Collisions.

Lagrangian Formulation: Classical, Single Particle, Klein-Gordon equation, Dirac equation, EM fields, the Standard Model

Symmetries: Groups, Noether’s Theorem & Conservation Laws

Classical and Quantum Statistical Mechanics: micro-, canonical, and grand Canonical ensembles, Many Body problems, Bosons (symmetric wavefunction), Fermions (anti-symmetric), Bose-Einstein condensation

Feynman Diagrams & QED: Introduction to Perturbation Theory, Introduction to Feynman Calculus, The Dirac Equation, The Photon, Diagrammatic Rules for QED

The Forces of Nature: The 4 forces, QED, QCD, Weak Force.

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6