Geodesic
Two-body problem on spaces of constant curvature: II.~Spectral properties of the Hamiltonian
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 481-489

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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 $\mathbb S^3$. 
@article{TMF_2000_124_3_a8,
     author = {I. \'E. Stepanova and A. V. Shchepetilov},
     title = {Two-body problem on spaces of constant curvature: {II.~Spectral} properties of the {Hamiltonian}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {481--489},
     publisher = {mathdoc},
     volume = {124},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a8/}
}
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I. É. Stepanova; A. V. Shchepetilov. Two-body problem on spaces of constant curvature: II.~Spectral properties of the Hamiltonian. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 481-489. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a8/