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Theoretical and Mathematical Physics

, Volume 198, Issue 3, pp 363–375 | Cite as

Threshold Phenomena in the Spectrum of the Two-Particle Schrödinger Operator on a Lattice

  • S. N. LakaevEmail author
  • A. T. Boltaev
Article
  • 5 Downloads

Abstract

For a broad class of short-range pairwise attraction potentials, we study threshold phenomena in the spectrum of the two-particle Schrödinger operator associated with the energy operator of the s–d exchange model. We prove that the bound state (eigenvalue) either exists or does not exist depending on the exchange interaction parameter, the system quasimomentum, and dimension of the lattice.

Keywords

discrete Schrödinger operator two-particle system energy operator dispersion relation virtual level eigenvalue lattice 

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Samarkand State UniversitySamarkandUzbekistan

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