Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length

Abstract

An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schrödinger equations on 3D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wavefunction for the hydrogen atom case. Finally, we make a comparison between the ``space curvature" effects and minimal length effects for the hydrogen spectrum