Elementary solutions of the quantum planar two center problem

The quantum problem of an electron moving in a plane under the field created by two Coulombian centers admits simple analytical solutions for some particular inter-center distances. These elementary eigenfunctions, akin to those found by Demkov for the analogous three dimensional problem, are calcul...

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Bibliographic Details
Published inarXiv.org
Main Authors Gonzalez Leon, M A, J Mateos Guilarte, M de la Torre Mayado
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.10.2017
Subjects
Eigenvectors
Exact solutions
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
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Summary:The quantum problem of an electron moving in a plane under the field created by two Coulombian centers admits simple analytical solutions for some particular inter-center distances. These elementary eigenfunctions, akin to those found by Demkov for the analogous three dimensional problem, are calculated using the framework of quasi-exact solvability of a pair of entangled ODE's descendants from the Heun equation. A different but interesting situation arises when the two centers have the same strength. In this case completely elementary solutions do not exist.
ISSN:2331-8422
DOI:10.48550/arxiv.1603.05454