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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.