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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 2, Pages 299–317
DOI: https://doi.org/10.4213/tmf6350 (Mi tmf6350) 		 
This article is cited in 15 scientific papers (total in 15 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
Full-text PDF (498 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf6350
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.
Received: 14.02.2008
Revised: 22.08.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 2, Pages 667–683
DOI: https://doi.org/10.1007/s11232-009-0054-y
Bibliographic databases:
Language: Russian
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
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    • This publication is cited in the following 15 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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