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Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice

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Abstract

We prove that the number of bound states for the Hamiltonian of a system of three arbitrary particles interacting through pairwise attraction potentials on a three-dimensional lattice is finite in the cases where (1) none of the two-particle subsystems has a virtual level and (2) only one of the two-particle subsystems has a virtual level.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Uzbekistan

    S. N. Lakaev & S. M. Samatov

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  1. S. N. Lakaev
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  2. S. M. Samatov
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Lakaev, S.N., Samatov, S.M. Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice. Theoretical and Mathematical Physics 129, 1655–1668 (2001). https://doi.org/10.1023/A:1013011300854

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  • DOI: https://doi.org/10.1023/A:1013011300854

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