Chemical Physics: the resident of the Institute of Quantum Physics Professor J.F.Ogilvie has published the article "The hydrogen atom in the momentum representation; a critique of the variables comprising the momentum representation"

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

J.R. Lombardi  J.F. Ogilvie Chemical Physics 2020

https://doi.org/10.1016/j.chemphys.2020.110886

The hydrogen atom seems to be a simple physical system comprising a negatively charged electron moving in the coulombic field of a positively charged proton. In the process of inventing wave mechanics, Schroedinger solved this problem by developing some functions in terms of the relative coordinates of the electron that yielded the energies of this system that were known from experiment. A major feature of wave mechanics is that it has two equivalent representations, with spatial coordinates as variables or components of momentum for that purpose. Until the present time, the solution of the Schroedinger equation in momentum variables has been problematic because the attempts to achieve that task generated functions that poorly reproduced known properties of the atom according to the coordinate representation. In the present work we have succeeded for the first time in devising a solution in momentum variables that can generate expectation values of distance and momentum exactly the same as have been long known for the functions in spatial variables. The new functions can be applied to various problems involving the interaction of light and other particles with a hydrogen atom.