skip to main content

Title: The Coulomb problem on a 3-sphere and Heun polynomials

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.
Authors:
 [1] ;  [1] ;  [2]
  1. INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati (Italy)
  2. (Armenia)
Publication Date:
OSTI Identifier:
22218151
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 8; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; COORDINATES; EIGENFUNCTIONS; EIGENVALUES; EQUATIONS; POLYNOMIALS; QUANTIZATION; QUANTUM MECHANICS; SPECTRA; SPHERES; VECTORS; WAVE FUNCTIONS