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TMF, 1998, Volume 116, Number 1, Pages 134–145 (Mi tmf893)  

This article is cited in 2 scientific papers (total in 2 papers)

Resonance multiplicity of a perturbed periodic Schrödinger operator

Yu. P. Chuburin

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We consider the perturbation of a periodic Schrödinger operator by a potential that is periodic in the variables $x_1$ and $x_2$ and exponentially decreases as $|x_3| \to \infty$. Near the zero surface of the derivative of the eigenvalue of the periodic operator in a cell with respect to the third quasi-momentum component, we obtain relations between the resonance multiplicity and the order of the pole of the quantities characterizing the scattering. As a rule, the forward scattering amplitude vanishes on this surface.

DOI: https://doi.org/10.4213/tmf893

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English version:
Theoretical and Mathematical Physics, 1998, 116:1, 846–855

Bibliographic databases:

Received: 20.02.1998

Citation: Yu. P. Chuburin, “Resonance multiplicity of a perturbed periodic Schrödinger operator”, TMF, 116:1 (1998), 134–145; Theoret. and Math. Phys., 116:1 (1998), 846–855

Citation in format AMSBIB
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\by Yu.~P.~Chuburin
\paper Resonance multiplicity of a~perturbed periodic Schr\"odinger operator
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\yr 1998
\vol 116
\issue 1
\pages 134--145
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\zmath{https://zbmath.org/?q=an:0952.47012}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 116
\issue 1
\pages 846--855
\crossref{https://doi.org/10.1007/BF02557127}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000076425700006}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. P. Chuburin, “Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film”, Theoret. and Math. Phys., 143:3 (2005), 836–847  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yu. P. Chuburin, “O dvumernom magnitnom operatore Shredingera v periodicheskom vneshnem pole”, Izv. IMI UdGU, 2006, no. 1(35), 77–82  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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