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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