Generalized coulomb Green's function for bound states of the nonrelativistic Schrödinger equation

The well-known closed expression for the Coulomb Green's function in the coordinate representation in terms of Whittaker functions is used to obtain an explicit expression for a generalized Coulomb Green's function for an arbitrary bound state of the nonretativistic Schrödinger equation in the three-dimensional case. Formulas are derived that express the corrections of the higher orders of perturbation theory in terms of the generalized Green's function.