This article is cited in 6 papers

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

I. É. Stepanova^a, A. V. Shchepetilov<sup>b

a</sup> Schmidt United Institute of Physics of the Earth, Russian Academy of Scienses
^b M. V. Lomonosov Moscow State University, Faculty of Physics

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 $\mathbb S^3$.

Received: 12.11.1999
Revised: 03.04.2000

DOI: 10.4213/tmf652

 English version: Theoretical and Mathematical Physics, 2000, 124:3, 1265–1272

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