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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 3, Pages 387–403
DOI: https://doi.org/10.4213/tmf6917 (Mi tmf6917) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice

M. É. Muminov, N. M. Aliev

Samarkand State University, Samarkand, Uzbekistan
Full-text PDF (442 kB) Citations (6)
References:
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DOI: https://doi.org/10.4213/tmf6917
Abstract: We consider a system of three arbitrary quantum particles on a one-dimensional lattice interacting pairwise via attractive contact potentials. We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum in the case where the masses of two particles are finite. We show that the discrete spectrum of the Schrödinger operator is infinite in the case where the masses of two particles in a three-particle system are infinite.
Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator.
Received: 24.05.2011
Revised: 06.09.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 3, Pages 754–768
DOI: https://doi.org/10.1007/s11232-012-0072-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. É. Muminov, N. M. Aliev, “Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice”, TMF, 171:3 (2012), 387–403; Theoret. and Math. Phys., 171:3 (2012), 754–768
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6917
  • https://doi.org/10.4213/tmf6917
  • https://www.mathnet.ru/eng/tmf/v171/i3/p387
    • This publication is cited in the following 6 articles:
    1. Zahriddin Muminov, Shukhrat Alladustov, “Threshold Analysis of the Schrödinger Operator of the System of Three Particles with Masses $m_1=m_2=\infty $ and $m_3<\infty $”, Complex Anal. Oper. Theory, 19:1 (2024)  crossref
    2. Z. I. Muminov, N. M. Aliev, T. Radjabov, “On the Discrete Spectrum of the Three-Particle Schrödinger Operator on a Two-Dimensional Lattice”, Lobachevskii J Math, 43:11 (2022), 3239  crossref
    3. S. N. Lakaev, A. R. Khalmukhamedov, A. M. Khalkhuzhaev, “Bound states of the Schrödinger operator of a system of three bosons on a lattice”, Theoret. and Math. Phys., 188:1 (2016), 994–1005  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. M. Muminov, H. Neidhardt, T. Rasulov, “On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case”, Journal of Mathematical Physics, 56:5 (2015)  crossref
    5. M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a $2\times2$ operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77  mathnet
    6. N. M. Aliev, M. E. Muminov, “On the spectrum of the three-particle Hamiltonian on a unidimensional lattice”, Siberian Adv. Math., 25:3 (2015), 155–168  mathnet  crossref  mathscinet
    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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    References:104
    First page:23
     
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