Two-body Coulomb problems with sources
G. GASANEO AND L. U. ANCARANI
PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS
AMER PHYSICAL SOC
Año: 2010 vol. 82 p. 1 - 8
The two-body Coulomb Schroedinger equation with different types of nonhomogeneities are studied. The o 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.