Hydrogen atom as an eigenvalue problem in 3-D spaces of constant curvatureand minimal length

An old result of Stevenson [Phys. Rev. 59, 842 (1941)] concerning the Keple r-Coulomb quantum problem on the three-dimensional (3-D) hypersphere is con sidered from the perspective of the radial Schrodinger equations on 3-D spa ces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wave function for the hydrogen atom case. Finally, we make a comparison between the "spa ce curvature" effects and minimal length effects for the hydrogen spectrum.