Two-body Coulomb problems with sources

Abstract

The two-body Coulomb Schrödinger equation with different types of nonhomogeneities are studied. The particular solution of these nonhomogeneous equations is expressed in closed form in terms of a two-variable hypergeometric function. A particular representation of the latter allows one to study efficiently the solution in the asymptotic limit of large values of the coordinate and hence the associated physics. Simple sources are first considered, and a complete analysis of scattering and bound states is performed. The solutions corresponding to more general (arbitrary) sources are then provided and written in terms of more general hypergeometric functions. © 2010 The American Physical Society.