Integral Representation for the Nonrelativistic Coulomb Green's Function

Although the radial Green's function for the Schrödinger equation in a Coulomb field can be obtained in the usual way in terms of the two linearly independent solutions to the radial equation for a particular angular momentum state, the sum over angular momentum states does not seem to have been carried out. In this note this sum is carried out and a ``closed form'' obtained in the form of a double integral. The result is believed to be useful for perturbation calculations where the ``intermediate states'' involve many angular momentum states.