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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 1, Pages 115–125
DOI: https://doi.org/10.4213/tmf6302 (Mi tmf6302) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential

Yu. P. Chuburin

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences
Full-text PDF (397 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf6302
Abstract: We consider a two-dimensional periodic Schrödinger operator perturbed by the interaction potential of two one-dimensional particles. We prove that quasilevels (i.e., eigenvalues or resonances) of the given operator exist for a fixed quasimomentum and a small perturbation near the band boundaries of the corresponding periodic operator. We study the asymptotic behavior of the quasilevels as the coupling constant goes to zero. We obtain a simple condition for a quasilevel to be an eigenvalue.
Keywords: two-particle Schrödinger operator, periodic potential, eigenvalue, resonance.
Received: 31.10.2007
Revised: 14.05.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 1, Pages 96–104
DOI: https://doi.org/10.1007/s11232-009-0007-5
Bibliographic databases:
Language: Russian
Citation: Yu. P. Chuburin, “Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential”, TMF, 158:1 (2009), 115–125; Theoret. and Math. Phys., 158:1 (2009), 96–104
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6302
  • https://doi.org/10.4213/tmf6302
  • https://www.mathnet.ru/eng/tmf/v158/i1/p115
    • This publication is cited in the following 2 articles:
    1. O. O. Pokutnyi, “Boundary-Value Problems for the Evolutionary Schrödinger Equation. I”, J Math Sci, 249:4 (2020), 647  crossref
    2. Yu. P. Chuburin, “Two-particle scattering in a periodic medium”, Theoret. and Math. Phys., 191:2 (2017), 738–751  mathnet  crossref  crossref  mathscinet  adsnasa  isi  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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    Abstract page:570
    Full-text PDF :227
    References:102
    First page:12
     
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