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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 3, Pages 438–451
DOI: https://doi.org/10.4213/tmf6937 (Mi tmf6937) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator

S. N. Lakaevab, A. M. Khalkhuzhaevba, Sh. S. Lakaevb

a Samarkand Branch, Uzbekistan Academy of Sciences, Samarkand, Uzbekistan
b Samarkand State University, Samarkand, Uzbekistan
Full-text PDF (427 kB) Citations (24)
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DOI: https://doi.org/10.4213/tmf6937
Abstract: We consider a two-particle discrete Schrödinger operator corresponding to a system of two identical particles on a lattice interacting via an attractive pairwise zero-range potential. We show that there is a unique eigenvalue below the bottom of the essential spectrum for all values of the coupling constant and two-particle quasimomentum. We obtain a convergent expansion for the eigenvalue.
Keywords: Hamiltonian, discrete Schrödinger operator, quasimomentum, essential spectrum, eigenvalue, asymptotic expansion, eigenvalue expansion, Fredholm determinant.
Received: 24.08.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 3, Pages 800–811
DOI: https://doi.org/10.1007/s11232-012-0076-8
Bibliographic databases:
Language: Russian
Citation: S. N. Lakaev, A. M. Khalkhuzhaev, Sh. S. Lakaev, “Asymptotic behavior of an eigenvalue of the two-particle discrete Schrödinger operator”, TMF, 171:3 (2012), 438–451; Theoret. and Math. Phys., 171:3 (2012), 800–811
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6937
  • https://doi.org/10.4213/tmf6937
  • https://www.mathnet.ru/eng/tmf/v171/i3/p438
    • This publication is cited in the following 24 articles:
    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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    References:117
    First page:21
     
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