Canonical partition function for the hydrogen atom in curved space

Abstract

The electronic partition function for the hydrogen atom was recently derived by integration over the Coulomb propagator. A much simpler derivation is given here, based on Schrödinger's exact solution for a hydrogenic atom in a Riemannian space of positive curvature. The energy spectrum is entirely discrete, including states which correspond to the ionized atom. The curvature in Riemannian space is shown to be equivalent to a finite volume in Euclidean space.