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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 182, Number 3, Pages 435–452
DOI: https://doi.org/10.4213/tmf8764 (Mi tmf8764) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice

M. I. Muminova, N. M. Alievb

a Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Malaysia
b Faculty of Mechanics and Mathematics, Samarkand State University, Samarkand, Republic Uzbekistan
Full-text PDF (474 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf8764
Abstract: We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.
Keywords: three-particle system on a lattice, Schrödinger operator, asymptotic number of eigenvalues, infinitely many eigenvalues in a gap in the essential spectrum, infinitely many eigenvalues in the essential spectrum.
Received: 04.07.2014
Revised: 04.09.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 182, Issue 3, Pages 381–396
DOI: https://doi.org/10.1007/s11232-015-0269-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. I. Muminov, N. M. Aliev, “Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice”, TMF, 182:3 (2015), 435–452; Theoret. and Math. Phys., 182:3 (2015), 381–396
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf8764
  • https://doi.org/10.4213/tmf8764
  • https://www.mathnet.ru/eng/tmf/v182/i3/p435
    • This publication is cited in the following 3 articles:
    1. Z. I. Muminov, Vasila Aktamova, “The Point Spectrum of the Three-Particle Schrödinger Operator on Z with Masses m1=m2=∞ and \boldsymbol{m_{3}<\infty}”, Lobachevskii J Math, 45:11 (2024), 5860  crossref
    2. N. M. Aliev, “Asymtotic of the Discrete Spectrum of the Three-Particle Schrödinger Operator on a One-Dimensional Lattice”, Lobachevskii J Math, 44:2 (2023), 491  crossref
    3. Sabirov O.Sh., Berdiyarov B.T., Yusupov A.Sh., Absalamov A.T., Berdibekov Adham Ilkhomjon Ugli, “Improving Ways to Increase the Attitude of the Investment Environment”, Rev. GEINTEC, 11:2 (2021), 1961–1975  crossref  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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    Abstract page:452
    Full-text PDF :176
    References:88
    First page:33
     
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