Wave functions of the Hydrogen atom in the momentum representation

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.

arXiv commentRevised version, according to the referees' suggestions. Includes new figures

References in corpus (7)

• Tunneling and delocalization in hydrogen bonded systems: a study in position and momentum space
• Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere
• A violation of the uncertainty principle implies a violation of the second law of thermodynamics
• Solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem (revisited)
• Hydrogen atom in phase space. The Kirkwood-Rihaczek representation
• Reflection above the barrier as tunneling in momentum space
• Some intricacies of the momentum operator in quantum mechanics