Wave functions of the Hydrogen atom in the momentum representation
Quantum Physics
2023-03-15 v2 Mathematical Physics
math.MP
Abstract
We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind, or in terms of (elementary) trigonometric functions. We show their symmetry under the group, and their equivalence with those of Lombardi and Oglivie.
Keywords
Cite
@article{arxiv.2208.13989,
title = {Wave functions of the Hydrogen atom in the momentum representation},
author = {M. Kirchbach and J. A. Vallejo},
journal= {arXiv preprint arXiv:2208.13989},
year = {2023}
}
Comments
Revised version, according to the referees' suggestions. Includes new figures