Harmonic oscillator Green’s function

Abstract

The Green’s function for the harmonic oscillator in three dimensions plays an important role in the theory of atomic collisions. One representation of low-energy ion–atom collisions involves harmonic oscillator potentials. A closed-form expression for the harmonic oscillator Green’s function, needed to exploit this representation, is derived. This expression is similar to the expression for the Coulomb Green’s function obtained by Hostler and Pratt. Calculations of electron distributions for a model system of ion–atom collisions are reported to illustrate the theory.