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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 56–60
DOI: https://doi.org/10.4213/faa204 (Mi faa204) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

S. A. Albeverioa, S. N. Lakaevb, Zh. I. Abdullaevb

a University of Bonn, Institute for Applied Mathematics
b A. Navoi Samarkand State University
Full-text PDF (143 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa204
Abstract: A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.
Keywords: Schrödinger equation, boson, Faddeev integral equation.
Received: 20.03.2000
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 3, Pages 212–216
DOI: https://doi.org/10.1023/A:1020226321856
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: S. A. Albeverio, S. N. Lakaev, Zh. I. Abdullaev, “On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 56–60; Funct. Anal. Appl., 36:3 (2002), 212–216
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa204
  • https://www.mathnet.ru/eng/faa/v36/i3/p56
    • This publication is cited in the following 5 articles:
    1. Ulugbek Soatov, Ulugbek Djanizoqov, Rustam Gadayev, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 030093  crossref
    2. T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895  mathnet  crossref  crossref  adsnasa  isi
    3. Rasulov T.H., “Investigations of the Essential Spectrum of a Hamiltonian in Fock Space”, Applied Mathematics & Information Sciences, 4:3 (2010), 395–412  mathscinet  isi
    4. M. I. Muminov, “A Hunziker–van Winter–Zhislin theorem for a four-particle lattice Schrödinger operator”, Theoret. and Math. Phys., 148:3 (2006), 1236–1250  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. S. N. Lakaev, Z. I. Muminov, “The Asymptotics of the Number of Eigenvalues of a Three-Particle Lattice Schrödinger Operator”, Funct. Anal. Appl., 37:3 (2003), 228–231  mathnet  crossref  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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