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Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice

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Abstract

We consider a system of three quantum particles interacting by pairwise short-range attraction potentials on a three-dimensional lattice (one of the particles has an infinite mass). We prove that the number of bound states of the corresponding Schrödinger operator is finite in the case where the potentials satisfy certain conditions, the two two-particle sub-Hamiltonians with infinite mass have a resonance at zero, and zero is a regular point for the two-particle sub-Hamiltonian with finite mass.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Uzbekistan

    M. E. Muminov

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  1. M. E. Muminov
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Correspondence to M. E. Muminov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 363–371, February, 2008.

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Muminov, M.E. Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice. Theor Math Phys 154, 311–318 (2008). https://doi.org/10.1007/s11232-008-0029-4

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  • DOI: https://doi.org/10.1007/s11232-008-0029-4

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