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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 170, Number 3, Pages 409–422
DOI: https://doi.org/10.4213/tmf6775 (Mi tmf6775) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Essential and discrete spectra of the three-particle Schrödinger operator on a lattice

Yu. Kh. Eshkabilov, R. R. Kucharov

Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
Full-text PDF (454 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf6775
Abstract: We study the position of the essential spectrum of a three-body Schrödinger operator H. We evaluate the lower boundary of the essential spectrum of H and prove that the number of eigenvalues located below the lower edge of the essential spectrum in the H model is finite.
Keywords: essential spectrum, discrete spectrum, lower boundary of the essential spectrum, Schrödinger operator.
Received: 01.04.2011
Revised: 01.07.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 170, Issue 3, Pages 341–353
DOI: https://doi.org/10.1007/s11232-012-0034-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, TMF, 170:3 (2012), 409–422; Theoret. and Math. Phys., 170:3 (2012), 341–353
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6775
  • https://doi.org/10.4213/tmf6775
  • https://www.mathnet.ru/eng/tmf/v170/i3/p409
    • This publication is cited in the following 6 articles:
    1. Kucharov R.R. Khamraeva R.R., “Non-Compact Perturbations of the Spectrum of Multipliers Given With Functions”, Nanosyst.-Phys. Chem. Math., 12:2 (2021), 135–141  crossref  isi
    2. Yu. Kh. Eshkabilov, R. R. Kucharov, “Partial integral operators of Fredholm type on Kaplansky–Hilbert module over $L_0$”, Vladikavk. matem. zhurn., 23:3 (2021), 80–90  mathnet  crossref
    3. Yu. Kh. Èshkabilov, “Spectrum of a model three-particle Schrödinger operator”, Theoret. and Math. Phys., 186:2 (2016), 268–279  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190  mathnet  crossref  mathscinet
    5. G. P. Arzikulov, Yu. Kh. Eshkabilov, “On the essential and the discrete spectra of a Fredholm type partial integral operator”, Siberian Adv. Math., 25:4 (2015), 231–242  mathnet  crossref  mathscinet
    6. Yu. Kh. Eshkabilov, “On the discrete spectrum of partial integral operators”, Siberian Adv. Math., 23:4 (2013), 227–233  mathnet  crossref  mathscinet  elib
    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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