School of Science
Department of Physics
18003
18003 Mathematical Physics
Course Webpage: https://eclass.uoa.gr/courses/PHYS230
Course Content
- Special functions and orthogonal polynomials. Expansion in eigenfunctions. Laplace, diffusion, Helmholtz, Poisson equations.
- Hilbert transform. Dispersion relations. Advanced complex integration techniques and their applications.
- Saddle point and stationary phase approximations. Asymptotic expansions.
- Green's functions: Construction of Green's functions for the Helmholtz, Poisson, Laplace equations and for the wave equation.
- Problems in Cartesian, spherical and cylindrical coordinates with homogeneous and inhomogeneous boundary conditions. Expansion in orthogonal polynomials. The importance of propagator and Green's function in quantum mechanics.
- Integral equations: Fredholm and Volterra equations. Relation to Green's equations. Exact solution techniques through expansion in orthogonal polynomials and through integral transformations (Fourier, Laplace, Mellin, Hankel). Solving through iterative approaches.