Two-body quantum mechanical problem on spheres

Abstract

The quantum mechanical two-body problem with a central interaction on the sphere ${\mathbf{S}}^n$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.

41 pages, no figures, typos corrected; appendix D was added

References in corpus (6)

• Essential self-adjointness of Schroedinger type operators on manifolds
• On reducing the Heun equation to the hypergeometric equation
• Coulomb-oscillator duality in spaces of constant curvature
• Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
• Two body problem on two point homogeneous spaces, invariant differential operators and the mass center concept
• Algebras of invariant differential operators on unit sphere bundles over two-point homogeneous Riemannian spaces