On the Use of Green Functions in Atomic and Molecular Calculations. I. The Green Function of the Hydrogen Atom

Abstract

It is customary to derive the quantum-mechanical theory of quasifree particles by means of Green-function techniques, making use of the Green function of a free particle. It is pointed out here that similar techniques can be used in atomic and molecular calculations if use is made of the Green function of the hydrogen atom, rather than the Green function of a free particle. The Green function of the hydrogen atom is derived by means of contour integrations in the complex plane, following previous work by Meixner. We also derive a slightly modified Green function which is adapted to perturbation calculations of the ground state. Both of these Green functions are obtained as expansions in terms of spherical harmonics; the radial functions are expressed in terms of confluent hypergeometric functions.