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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 164, Number 1, Pages 46–61
DOI: https://doi.org/10.4213/tmf6523 (Mi tmf6523) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice

M. I. Muminovab

a Samarkand State University, Samarkand, Uzbekistan
b Department of Mathematics, Dogus University, Istanbul, Turkey
Full-text PDF (452 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf6523
Abstract: We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schrödinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.
Keywords: discrete spectrum, essential spectrum, Schrödinger operator, positive operator, compact operator.
Received: 13.11.2009
Revised: 16.12.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 164, Issue 1, Pages 869–882
DOI: https://doi.org/10.1007/s11232-010-0069-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. I. Muminov, “Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice”, TMF, 164:1 (2010), 46–61; Theoret. and Math. Phys., 164:1 (2010), 869–882
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6523
  • https://doi.org/10.4213/tmf6523
  • https://www.mathnet.ru/eng/tmf/v164/i1/p46
    • This publication is cited in the following 3 articles:
    1. Mukhiddin I. Muminov, S. K. Ghoshal, “Spectral Attributes of Self-Adjoint Fredholm Operators in Hilbert Space: A Rudimentary Insight”, Complex Anal. Oper. Theory, 13:3 (2019), 1313  crossref
    2. 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
    3. M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a 2×2 operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :215
    References:90
    First page:11
     
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