Green’s Functions of the Single-Particle Schrödinger Equation

Abstract

In the theory of interacting systems the Green’s function, or propagator, plays a crucial role. In its basic definition it is a much more complex function than the “simple” Green’s function, familiar from the theory of partial differential equations, but many of its properties do bear a very close relationship to the simple function. It is worthwhile, therefore, to review our theory of Green’s functions within the framework of the Schrödinger equation and perturbation theory. In this way we can introduce more of the concepts that appear in the full theory of interacting systems within a well-understood framework.