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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 143, Number 3, Pages 417–430
DOI: https://doi.org/10.4213/tmf1822 (Mi tmf1822) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film

Yu. P. Chuburin

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences
Full-text PDF (266 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf1822
Abstract: We obtain formulas for resonances and eigenvalues embedded in the continuous spectrum that are similar to formulas in the standard perturbation theory. We prove that although the imaginary part of the first-order correction to the eigenvalue embedded in the continuous spectrum is zero, the perturbed eigenfunction, as a rule, ceases to be square-summable.
Keywords: Schrodinger operator, perturbation theory, resonance, eigenvalue.
Received: 08.09.2004
Revised: 24.01.2005
English version:
Theoretical and Mathematical Physics, 2005, Volume 143, Issue 3, Pages 836–847
DOI: https://doi.org/10.1007/s11232-005-0109-7
Bibliographic databases:
Language: Russian
Citation: Yu. P. Chuburin, “Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film”, TMF, 143:3 (2005), 417–430; Theoret. and Math. Phys., 143:3 (2005), 836–847
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf1822
  • https://doi.org/10.4213/tmf1822
  • https://www.mathnet.ru/eng/tmf/v143/i3/p417
    • This publication is cited in the following 3 articles:
    1. Kondej S., “Straight Quantum Layer With Impurities Inducing Resonances”, J. Phys. A-Math. Theor., 50:31 (2017), 315203  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Kondej S., “Resonances Induced by Broken Symmetry in a System with a Singular Potential”, Ann. Henri Poincare, 13:6 (2012), 1451–1467  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Yu. P. Chuburin, “Decay law for a quasistationary state of the Schrödinger operator for a crystal film”, Theoret. and Math. Phys., 151:2 (2007), 648–658  mathnet  crossref  crossref  mathscinet  zmath  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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    References:106
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