The Coulomb problem on a 3-sphere and Heun polynomials
High Energy Physics - Theory
2015-06-12 v3 Mathematical Physics
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1302.0798,
title = {The Coulomb problem on a 3-sphere and Heun polynomials},
author = {Stefano Bellucci and Vahagn Yeghikyan},
journal= {arXiv preprint arXiv:1302.0798},
year = {2015}
}
Comments
8 pages, PACS 03.65.-w, 02.30.Ik, 14.80.Hv; typo in eqs. (9) and (12) corrected