The Coulomb problem on a 3-sphere and Heun polynomials
arXiv:1302.0798 · doi:10.1063/1.4817487
Abstract
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.
8 pages, PACS 03.65.-w, 02.30.Ik, 14.80.Hv; typo in eqs. (9) and (12) corrected