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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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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