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This subject will introduce topics in Theoretical Physics, including:
- Classical Field Theory: Action Principles and Noether’s Theorem. Electrodynamics and wave equations from action principle. Applications selected from: waves in media, dispersion relations, solitons, Kramers-Kronig relations, the Optical Theorem.
- Fluid Mechanics: Euler’s equation, the continuity equation and the Navier-Stokes equation. Rotational and irrotational flows. Turbulence and Reynolds’ numbers, and the onset of chaos. The Rayleigh-Taylor and other instabilities. Shock waves. The Kutta-Joukowski theorem and aerodynamics.
- Symmetry: Crystallography, point groups and space groups. Quasicrystals. Vibrational modes of molecules and molecular electronic structure. Crystal field theory. The uses of SU(2) in quantum mechanics. The SO(4) solution of the hydrogen atom. Relativistic invariance: the Lorentz and Poincare groups.
Intended learning outcomes
On completing this subject the student will be able to
- apply action principles to the physics of the fields involved in electrodynamics and continuous media.
- solve the basic equations of fluid flow, turbulence and aerodynamics.
- apply symmetry principles to problems involving a diverse range of physical systems and describe their connection to conservation laws.
A student who completes this subject should be able to:
- analyse how to solve a problem by applying fundamental laws to more complicated situations
- apply abstract concepts to real world situations
- solve relatively complicated problems using approximations
- participate effectively in group discussions
- manage time effectively in order to be prepared for group discussions and to undertake written assignments and examinations.
Last updated: 8 November 2019