Classical and quantum mechanical two body problem with central interaction on simply connected spaces of constant sectional curvature

The classical and quantum problems of two particles with central interaction on simply connected spaces of a constant curvature are considered. The reduction of classical problem to the dynamic systems in four-dimensional phase space are carried out using Marsden-Weinstein method. The classification of reduced dynamic systems was given. By using isometry group, in quantum case, systems of ordinary differential equations for energy levels are obtained. For the sphere in the case of equal masses some energy levels are calculated.