Related papers: Wave functions of the Hydrogen atom in the momentum representation

Wave functions of the Hydrogen atom in the momentum representation

URL: http://arxiv.org/abs/2208.13989v2
Date: Thu, 19 Jan 2023 01:55:21 GMT
Title: Wave functions of the Hydrogen atom in the momentum representation
Authors: M. Kirchbach and J. A. Vallejo
Abstract summary: radial wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind. We show their symmetry under the $SO(4)$ group, and their equivalence with those of Lombardi and Oglivie.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 $SO(4)$ group, and their equivalence with those of Lombardi and Oglivie.

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