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

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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\(\mathbb{S}^3 \).

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Authors and Affiliations

  1. Joint Institute for Physics of Earth, RAS, Moscow, Russia

    I. É. Stepanova

  2. Moscow State University, Moscow, Russia

    A. V. Shchepetilov

Authors
  1. I. É. Stepanova
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  2. A. V. Shchepetilov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 481–489, September, 2000.

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Stepanova, I.É., Shchepetilov, A.V. Two-body problem on spaces of constant curvature: II. Spectral properties of the Hamiltonian. Theor Math Phys 124, 1265–1272 (2000). https://doi.org/10.1007/BF02551003

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  • DOI: https://doi.org/10.1007/BF02551003

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