GENERALIZED STURMIAN EXPANSIONS OF COULOMB GREENS-FUNCTIONS AND 2-PHOTON GORDON FORMULA

A useful representation for the radial part of the Coulomb Green's fun ction is derived in the form of a double series in Laguerre polynomial s with two free (arbitrary) parameters alpha and alpha'. An appropriat e choice of alpha and alpha' leads to a cardinal simplification in cal culations of matrix elements involving Green's functions. The results are valid both in the nonrelativistic and in the relativistic case of the second-order Dine equation. The momentum form of the nonrelativist ic Green's function with free parameters is presented and a simple exa mple of a two-photon extension of the well-known Gordon formula is giv en. (C) 1998 Published by Elsevier Science B.V.