The sums of products of Coulomb wave function over degenerate states are ex
pressed in terms of quadratic forms that depend on the wave function of onl
y one state with zero orbital angular momentum l = m = 0. These sums are en
countered in many fields in the physics of atoms and molecules, for example
, in investigations of the perturbation of degenerate atomic energy levels
of a small potential well, a delta-function potential. The sums were found
in an investigation of the limit of the Coulomb Green's function G(r, r', E
), where the energy parameter E approaches an atomic energy level: E --> E-
n, E-n = -Z(2)/2n(2). The Green's function found by L. Hostler and R. Pratt
in 1963 was used. The result obtained is a consequence of the degeneracy o
f the Coulomb energy levels, which in turn is due to the four-dimensional s
ymmetry of the Coulomb problem. (C) 2000 MAIK "Nauka/Interperiodica".