These notes accompanied a course I gave at the Max Planck Institute for Festkörperforschung, Stuttgart in 2002. They are a somewhat short-hand overview of how to obtain Green functions from differential equations in general. I include a discussion of the notorious self-interaction term.

Most interesting to me personally is the application of Green functions to optical scattering problems. Therefore I concentrate in the second part of the notes on optical scattering problems and how to solve them using Green functions. Starting ab-initio from the Maxwell equations, the complete way up to numerical evaluations in the discrete dipole approximation is delineated.

GreensFunctionsAndMaxwell.pdf