The hydrogen atom in the momentum representation; a critique of the variables comprising the momentum representation

We examine critically the solutions for the hydrogen atom in momentum space. We demonstrate that the approach by Podolsky and Pauling (Physical Review 1928, 34, 109) to such a transformation was inconsistent with Podolsky's preceding analysis (Physical Review 1928, 32, 812) and yields functions that fail to utilize quantum-mechanically acceptable variables in momentum space. This practice arose from the commonplace belief that functions in momentum space are Fourier transforms of those in position space. We show that proper quantum-mechanical functions are obtainable through presentation of a clear definition of momentum space based on DeWitt's transformation (Physical Review 1952, 85, 653). This method allows us to obtain proper wave functions for the hydrogen atom in momentum space.