Partial-wave Green-function expansions for general potentials

Abstract

We present a derivation of the partial-wave expansions of the exact, time-independent, single-particle Green function for an arbitrary potential taken from a wide class typical of atomic and molecular systems, whose expansion in spherical harmonics about some point is given. The Green-function expansions are expressed in terms of matrix solutions, one regular at the origin and one at infinity, of the coupled radial Schroedinger equations related to that potential, and a constant, Wronskian-type matrix constructed from them. Expansions are developed for both positive energies, relevant to scattering states, and negative energies, where we elucidate the mathematical condition for bound state000.