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Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice

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Abstract

We consider a system of three arbitrary quantum particles on a one-dimensional lattice interacting pairwise via attractive contact potentials. We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum in the case where the masses of two particles are finite. We show that the discrete spectrum of the Schrödinger operator is infinite in the case where the masses of two particles in a three-particle system are infinite.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Uzbekistan

    M. É. Muminov & N. M. Aliev

Authors
  1. M. É. Muminov
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  2. N. M. Aliev
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Correspondence to M. É. Muminov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 171, No. 3, pp. 387–403, June, 2012.

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Muminov, M.É., Aliev, N.M. Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice. Theor Math Phys 171, 754–768 (2012). https://doi.org/10.1007/s11232-012-0072-z

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  • DOI: https://doi.org/10.1007/s11232-012-0072-z

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