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TMF, 2008, Volume 154, Number 2, Pages 363–371 (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

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

DOI: https://doi.org/10.4213/tmf6175

Full text: PDF file (376 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 154:2, 311–318

Bibliographic databases:

Received: 21.02.2007

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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  • http://mi.mathnet.ru/eng/tmf6175
  • https://doi.org/10.4213/tmf6175
  • http://mi.mathnet.ru/eng/tmf/v154/i2/p363

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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