Green’s Functions and Perturbation Theory

Abstract

The problem of finding the eigenvalues and eigenfunctions of a Hamiltonian ℌ = ℌ0 + ℌ1 can be solved in three steps: 1) Calculate the Green’s function G0(z) corresponding to ℌ0. 2) Express G(z) as a perturbation series in terms of G0(z) and ℌ1, where G(z) is the Green’s function associated with ℌ. 3) Extract from G(z) information about the eigenvalues and eigenfunctions of ℌ.