The Green’s function for the two-center system with coulomb interaction
Abstract:
Semi-analytical representations (by the way of partial expansions)
for a radial part of a Green's function for two identical Coulomb centers
are obtained. Two types of expansions are built for regular and irregular
radial Coulomb spheroidal functions: over the Coulomb radial functions
and over the solutions of a confluent hypergeometric equation. The problem
of convergence of these expansions is studied in detail and are explained
formal fundamentalses of a computing procedure for solution to the related
them infinite three-terms recurrent relations. The asymptotic formulas
for permissible parameters n are obtained at
R® 0 to within the O(R3) terms
and at R® ¥
to within the O(1/R3) terms.