Path integral treatment of the hydrogen atom in a curved space of constant curvature

Abstract

The path integral treatment of the hydrogen atom in a spherical space is discussed. The dynamical group SU(1,1) of the system is used for path integration. By mapping the radial path integral onto the SU(1,1) manifold, the energy spectrum and the normalised wavefunctions are obtained. In the flat space limit, the standard hydrogen spectrum and the corresponding normalised energy eigenfunctions are recovered. The scattering states are also found in the limit.