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TMF, 2009, Volume 159, Number 2, Pages 299–317 (Mi tmf6350)  

This article is cited in 10 scientific papers (total in 10 papers)

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

M. I. Muminov

A. Navoi Samarkand State University

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.

Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator

DOI: https://doi.org/10.4213/tmf6350

Full text: PDF file (498 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 159:2, 667–683

Bibliographic databases:

Received: 14.02.2008
Revised: 22.08.2008

Citation: M. I. Muminov, “The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice”, TMF, 159:2 (2009), 299–317; Theoret. and Math. Phys., 159:2 (2009), 667–683

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6350
  • http://mi.mathnet.ru/eng/tmf/v159/i2/p299

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. I. Muminov, “Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 164:1 (2010), 869–882  mathnet  crossref  crossref  adsnasa  isi
    2. M. É. Muminov, N. M. Aliev, “Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice”, Theoret. and Math. Phys., 171:3 (2012), 754–768  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. M. I. Muminov, A. M. Hurramov, “Spectral properties of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 177:3 (2013), 1693–1705  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a $2\times2$ operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77  mathnet
    5. M. I. Muminov, A. M. Hurramov, “Multiplicity of virtual levels at the lower edge of the continuous spectrum of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 180:3 (2014), 1040–1050  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. N. M. Aliev, M. E. Muminov, “On the spectrum of the three-particle Hamiltonian on a unidimensional lattice”, Siberian Adv. Math., 25:3 (2015), 155–168  mathnet  crossref  mathscinet
    7. M. I. Muminov, N. M. Aliev, “Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 182:3 (2015), 381–396  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Muminov M.I. Lokman C., “Finiteness of Discrete Spectrum of the Two-Particle Schrodinger Operator on Diamond Lattices”, Nanosyst.-Phys. Chem. Math., 8:3 (2017), 310–316  crossref  isi
    9. Kholmatov Sh.Yu. Muminov Z.I., “Existence of Bound States of N-Body Problem in An Optical Lattice”, J. Phys. A-Math. Theor., 51:26 (2018), 265202  crossref  isi  scopus  scopus
    10. Muminov M.I. Ghoshal S.K., “Spectral Attributes of Self-Adjoint Fredholm Operators in Hilbert Space: a Rudimentary Insight”, Complex Anal. Oper. Theory, 13:3 (2019), 1313–1323  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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