A Note on the Generating Function for the Coulomb Wave Functions

Abstract

An attempt is made to find a generating function for the radial wave functions in the quantum mechanical Kepler problem. It is shown that for the Mellin-transformed Coulomb wave functions with a fixed angular momentum, a generating function can be represented as a double integral form. The s-wave case is studied in more detail. The generating function is simplified to a single integral form, by which the orthogonality property of the original functions is reduced to that of a new series of functions. The properties of these functions are briefly discussed.