Two-body problem on spaces of constant curvature: II. Spectral properties of the Hamiltonian

Abstract

We consider the problem of two bodies with a central interaction on simply connected constant-curvature spaces of arbitrary dimension. We construct the self-adjoint extension of the quantum Hamiltonian, which was explicitly expressed through the radial differential operator and the generators of the isometry group of a configuration space in Part I of this paper. Exact spectral series are constructed for several potentials in the space $$\mathbb{S}^3 $$ .