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Finiteness of the discrete spectrum of the three-particle schrödinger equation on a lattice

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Abstract

Consideration is given to the Hamiltonian of a system of three identical quantum particles on a lattice that interact via pairwise contact attractive potentials. Finiteness of the three-particle bound states is proved for the three-dimensional discrete Schrödinger operator on the condition that the operators describing the two-particle subsystems have no virtual levels. For high dimensions (v ≥ 5), the finiteness of three-particle bound states is also proved in the presence of virtual levels.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Republic of Uzbekistan

    Zh. I. Abdullaev & S. N. Lakaev

Authors
  1. Zh. I. Abdullaev
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  2. S. N. Lakaev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 94–108, April, 1997.

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Abdullaev, Z.I., Lakaev, S.N. Finiteness of the discrete spectrum of the three-particle schrödinger equation on a lattice. Theor Math Phys 111, 467–479 (1997). https://doi.org/10.1007/BF02634201

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  • DOI: https://doi.org/10.1007/BF02634201

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