The hydrogen atom in momentum space

To complement the existing descriptions of amplitude functions for the hydrogen atom in the coordinate representation in various systems, we present all known and well characterised amplitude functions in the corresponding momentum representation, specifically according to the treatments of Podolsky and Pauling on transformation from spherical polar coordinates, of Klein on a transformation analogous to that from paraboloidal coordinates, and of Lombardi on transformations from both spherical polar and paraboloidal coordinates. Figures depicting surfaces of the functions in their real and imaginary parts or their squares illustrate the diversity of shapes of these surfaces according to the various momentum variables. (author)