Common Generating Function for Three-Dimensional Hydrogen Atom Complete Wave Functions

摘要

The Schrodinger equation for the three-dimensional hydrogen atom is separable and integrable in spherical, spheroconal, parabolic, and prolate spheroidal coordinates. The formal correspondence of the eigenfunctions in parabolic coordinates with two harmonic-oscillator eigenfunctions in circular coordinates leads to the identification of a generating function for the hydrogen atom eigenfunctions. Its expansions yielding the complete wave functions in the respective coordinates are explicitly constructed. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 790-800, 2009