Elementary solutions of the quantum planar two-center problem
1 Departamento de Matemática Aplicada, Universidad de Salamanca - Salamanca, Spain
2 Departamento de Física Fundamental, Universidad de Salamanca - Salamanca, Spain
Received: 5 April 2016
Accepted: 18 May 2016
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 intercenter 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.
PACS: 03.65.Ge – Solutions of wave equations: bound states / 02.30.Ik – Integrable systems / 31.15.-p – Calculations and mathematical techniques in atomic and molecular physics
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