INVARIANT TREATMENT OF THE TWO-BODY PROBLEM WITH CENTRAL INTERACTION ON SIMPLY CONNECTED SPACES OF CONSTANT SECTIONAL CURVATURE

The classical and quantum problems of two particles with central Ainteraction on simply connected spaces of a constant curvature with an Aarbitrary dimension are considered from the coordinate-free point of Aview. We give a representation of Hamiltonians via generators of the Asymmetry group. Some ordinary differential equations for energy levels Aof this system are obtained. For some potentials these levels are Acalculated explicitly.