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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 3, Pages 415–431
DOI: https://doi.org/10.4213/tmf546 (Mi tmf546) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice

S. N. Lakaeva, S. M. Samatov

a A. Navoi Samarkand State University
Full-text PDF (289 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf546
Abstract: We prove that the number of bound states for the Hamiltonian of a system of three arbitrary particles interacting through pairwise attraction potentials on a three-dimensional lattice is finite in the cases where (1) none of the two-particle subsystems has a virtual level and (2) only one of the two-particle subsystems has a virtual level.
Received: 10.01.2001
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 3, Pages 1655–1668
DOI: https://doi.org/10.1023/A:1013011300854
Bibliographic databases:
Language: Russian
Citation: S. N. Lakaev, S. M. Samatov, “Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice”, TMF, 129:3 (2001), 415–431; Theoret. and Math. Phys., 129:3 (2001), 1655–1668
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf546
  • https://doi.org/10.4213/tmf546
  • https://www.mathnet.ru/eng/tmf/v129/i3/p415
    • This publication is cited in the following 7 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
    3. Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. S. M. Tashpulatov, “Spectrum of the energy operator of a two-magnon system in the three-dimensional isotropic Heisenberg ferromagnet model with impurity”, Theoret. and Math. Phys., 162:2 (2010), 188–200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Albeverio, S, “THE ESSENTIAL AND DISCRETE SPECTRUM OF A MODEL OPERATOR ASSOCIATED TO A SYSTEM OF THREE IDENTICAL QUANTUM PARTICLES”, Reports on Mathematical Physics, 63:3 (2009), 359  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Albeverio, S, “On the structure of the essential spectrum for the three-particle Schrodinger operators on lattices”, Mathematische Nachrichten, 280:7 (2007), 699  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Albeverio, S, “Schrodinger operators on lattices. The Efimov effect and discrete spectrum asymptotics”, Annales Henri Poincare, 5:4 (2004), 743  crossref  mathscinet  zmath  isi  scopus
    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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