On the degeneracy of the energy levels of Schrödinger and Klein-Gordon equations on Riemannian coverings

Abstract We study the degeneracy of the energy levels of the Schrödinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the Schwarzschild space-time respectively. Degeneracy of energy levels is a consequence of the superintegrability of the system. We see how the degree of degeneracy changes depending on the covering parameter k , the parameter that in space-times can be related with a cosmic string, and show examples of lower degeneracy in correspondence of non integer values of k .