Geodesic
Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 248-263

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We consider the quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces. Using the group isometries, we obtain systems of ordinary differential equations for the energy levels. We prove that the Hamiltonian is self-adjoint for several interaction potentials. For the sphere, a number of energy series are evaluated for bodies with equal masses. 
@article{TMF_1999_118_2_a5,
     author = {A. V. Shchepetilov},
     title = {Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {248--263},
     publisher = {mathdoc},
     volume = {118},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a5/}
}
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A. V. Shchepetilov. Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 248-263. http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a5/