Coulomb Green's Function in f-Dimensional Space

Abstract

It is shown that the f‐dimensional nonrelativistic Coulomb Green's function and the associated reduced Green's functions can be obtained by differentiation of the corresponding functions in the 1‐dimensional (f odd) or 2‐dimensional (f even) case. A new expansion of the 3‐dimensional coordinate‐space Coulomb Green's function and a new sum formula for a product of two Laguerre polynomials with different arguments are derived.