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2008•International Journal of Quantum ChemistryRequires access

Common generating function for three‐dimensional hydrogen atom complete wave functions

E. Ley‐Koo, Araceli Góngora

Open publisher page 8 citations

Abstract

Abstract The Schrödinger 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. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

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What this paper is about

Abstract The Schrödinger 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. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

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Available abstract

Abstract The Schrödinger 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. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Key concepts: Eigenfunction, Prolate spheroidal coordinates, Parabolic coordinates, Hydrogen atom, Wave function, Harmonic oscillator, Elliptic coordinate system, Bipolar coordinates

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