2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101984The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ 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 addedMathematical Physics43A85, 22E70, 57S25, 70G65text