Green’s Functions and Perturbation Theory

Abstract

In this chapter we are interested in finding the eigenvalues and eigenfunctions of a hamiltonian H which can be decomposed as

$$ H = {H_0} + {H_1}; $$

((4.1))

H ₀ is such that its eigenvalues and eigenfunctions can be easily determined. This problem will be solved by: 1) calculating G ₀(z) corresponding to H ₀ ; 2) expressing G(z) in terms of G ₀(z) and H ₁, where G(z) is the Green’s function associated with H; and 3) extracting from G(z) information about the eigenvalues and eigenfunctions of H.