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

This article is cited in 5 scientific papers (total in 5 papers)

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:

Received: 05.06.1998

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
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\paper Quantum mechanical two-body problem with central interaction on simply connected constant-curvature surfaces
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\issue 2
\pages 248--263
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 2
\pages 197--208
\crossref{https://doi.org/10.1007/BF02557312}
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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  adsnasa  isi
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Shchepetilov, AV, “The two-body quantum mechanical problem on spheres”, Journal of Physics A-Mathematical and General, 39:15 (2006), 4011  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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