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 TMF, 1999, Volume 118, Number 2, Pages 248–263 (Mi tmf697)

Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces

A. V. Shchepetilov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: 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.

DOI: https://doi.org/10.4213/tmf697

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English version:
Theoretical and Mathematical Physics, 1999, 118:2, 197–208

Bibliographic databases:

Citation: A. V. Shchepetilov, “Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces”, TMF, 118:2 (1999), 248–263; Theoret. and Math. Phys., 118:2 (1999), 197–208

Citation in format AMSBIB
\Bibitem{Shc99} \by A.~V.~Shchepetilov \paper Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces \jour TMF \yr 1999 \vol 118 \issue 2 \pages 248--263 \mathnet{http://mi.mathnet.ru/tmf697} \crossref{https://doi.org/10.4213/tmf697} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702931} \zmath{https://zbmath.org/?q=an:0966.81013} \transl \jour Theoret. and Math. Phys. \yr 1999 \vol 118 \issue 2 \pages 197--208 \crossref{https://doi.org/10.1007/BF02557312} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079807100006} 

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• https://doi.org/10.4213/tmf697
• http://mi.mathnet.ru/eng/tmf/v118/i2/p248

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This publication is cited in the following articles:
1. A. V. Shchepetilov, “Two-body problem on spaces of constant curvature: I. Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system”, Theoret. and Math. Phys., 124:2 (2000), 1068–1081
2. I. É. Stepanova, A. V. Shchepetilov, “Two-body problem on spaces of constant curvature: II. Spectral properties of the Hamiltonian”, Theoret. and Math. Phys., 124:3 (2000), 1265–1272
3. Shchepetilov, AV, “Invariant treatment of the two-body problem with central interaction on simply connected spaces of constant sectional curvature”, Reports on Mathematical Physics, 46:1–2 (2000), 245
4. Shchepetilov, A, “Two-body problem on two-point homogeneous spaces, invariant differential operators and the mass center concept”, Journal of Geometry and Physics, 48:2–3 (2003), 245
5. Shchepetilov, AV, “The two-body quantum mechanical problem on spheres”, Journal of Physics A-Mathematical and General, 39:15 (2006), 4011
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