Methods of Mathematical Physics (MAST30031)

This subject gives an example-oriented overview of various advanced topics that are important for mathematical physics and physics students, as well as being of interest to students of pure and applied mathematics. These topics include:

• Further differential equations: Bessel functions, Legendre polynomials, spherical harmonics and applications such as the Laplace/Schrodinger equation in polar/spherical coordinates;
• Further vector calculus: Differential forms, integration, Stokes’ theorem and applications such as Maxwell’s equations, charge conservation and Dirac monopoles;
• Hilbert spaces: L2 spaces, bounded and unbounded operators, normalisable and non-normalisable eigenfunctions, distributions and applications to quantum theory;
• Group theory: Lie groups and algebras, representations and applications such as quantum spin and particle physics.