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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 2, Pages 363–371
DOI: https://doi.org/10.4213/tmf6175 (Mi tmf6175) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice

M. I. Muminov

A. Navoi Samarkand State University
Full-text PDF (376 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf6175
Abstract: We consider a system of three quantum particles interacting by pairwise short-range attraction potentials on a three-dimensional lattice (one of the particles has an infinite mass). We prove that the number of bound states of the corresponding Schrödinger operator is finite in the case where the potentials satisfy certain conditions, the two two-particle sub-Hamiltonians with infinite mass have a resonance at zero, and zero is a regular point for the two-particle sub-Hamiltonian with finite mass.
Keywords: resonance, two-particle sub-Hamiltonian, discrete spectrum, variation principle.
Received: 21.02.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 2, Pages 311–318
DOI: https://doi.org/10.1007/s11232-008-0029-4
Bibliographic databases:
Language: Russian
Citation: M. I. Muminov, “Finiteness of the discrete spectrum of the Schrödinger operator of three particles on a lattice”, TMF, 154:2 (2008), 363–371; Theoret. and Math. Phys., 154:2 (2008), 311–318
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6175
  • https://doi.org/10.4213/tmf6175
  • https://www.mathnet.ru/eng/tmf/v154/i2/p363
    • This publication is cited in the following 2 articles:
    1. M. E. Muminov, E. M. Shermatova, “On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 60:1 (2016), 22–29  mathnet  crossref  isi
    2. Rasulov T.H., “on the Finiteness of the Discrete Spectrum of a 3 X 3 Operator Matrix”, Methods Funct. Anal. Topol., 22:1 (2016), 48–61  mathscinet  zmath  isi
    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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