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 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. 
M. A. Gonzalez Leon, J. Mateos Guilarte and M. de la Torre Mayado
math-ph math.MP quant-ph