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arXiv · 1603.05454

Elementary solutions of the quantum planar two center problem

M. A. Gonzalez Leon·J. Mateos Guilarte·M. de la Torre Mayado
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Abstract

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.

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M. A. Gonzalez Leon, J. Mateos Guilarte, M. de la Torre Mayado. 2016-03-17. Elementary solutions of the quantum planar two center problem. https://doi.org/10.1209/0295-5075%2F114%2F30007

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