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The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice

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Abstract

We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.

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Authors and Affiliations

  1. Alisher Navoi 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. 159, No. 2, pp. 299–317, May, 2009.

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Muminov, M.E. The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice. Theor Math Phys 159, 667–683 (2009). https://doi.org/10.1007/s11232-009-0054-y

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  • DOI: https://doi.org/10.1007/s11232-009-0054-y

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