These notes accompanied a course I gave at the Max Planck Institute for Festkörperforschung, Stuttgart in 2003. They are a somewhat short-hand overview of how Green functions appear in many corners of physics and other areas which use differential equations. First I discuss some more general properties of Green functions, e.g., how they relate to local density of states, and how to use them to obtain particular solutions. After the derivation of Green functions for the fundamental Laplace operator (relevant to practically all wave phenomena) in 1,2,3 dimensions, I briefly discuss the connection of Green functions with perturbation theory and scattering problems.

Most interesting to me personally is the application of Green functions to optical scattering problems. While I touch upon this in one Section, I have worked out this particular topic in more detail in a separate document.

GreenFunctions.pdf