Elementary solutions of the quantum planar two center problem
Mathematical Physics
2017-10-03 v2 math.MP
Quantum Physics
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.
Cite
@article{arxiv.1603.05454,
title = {Elementary solutions of the quantum planar two center problem},
author = {M. A. Gonzalez Leon and J. Mateos Guilarte and M. de la Torre Mayado},
journal= {arXiv preprint arXiv:1603.05454},
year = {2017}
}
Comments
Revised version. 10 pages, 4 figures