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Sbornik: Mathematics, 2009, Volume 200, Issue 12, Pages 1847–1880
DOI: https://doi.org/10.1070/SM2009v200n12ABEH004062 (Mi sm7579) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The resonance spectrum of a Schrödinger operator with a rapidly decaying potential

S. A. Stepinab, A. G. Tarasova

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Bialystok
English version PDF (439 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM2009v200n12ABEH004062
Abstract: Resonances of the one-dimensional Schrödinger operator are investigated, that is, the poles of the analytic extension of the corresponding scattering matrix. For a certain class of superexponentially decreasing potentials, including the Gaussian potential, the Born approximation is substantiated for the problem of localizing the poles of the scattering matrix. This makes it possible to find an asymptotic law (a quantization rule) for the distribution of these poles. For the first time, using the method developed in the paper, asymptotic formulae for resonances are obtained in the case of potentials with noncompact support.
Bibliography: 15 titles.
Keywords: resonance, pole of a scattering matrix, asymptotic distribution, Schrödinger operator, superexponentially decreasing potential.
Received: 18.05.2009 and 08.07.2009
Bibliographic databases:
UDC: 517.927
MSC: Primary 34L25, 34L40; Secondary 47E05
Language: English
Original paper language: Russian
Citation: S. A. Stepin, A. G. Tarasov, “The resonance spectrum of a Schrödinger operator with a rapidly decaying potential”, Sb. Math., 200:12 (2009), 1847–1880
Citation in format AMSBIB
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\by S.~A.~Stepin, A.~G.~Tarasov
\paper The resonance spectrum of a Schr\"odinger operator with a rapidly decaying potential
\jour Sb. Math.
\yr 2009
\vol 200
\issue 12
\pages 1847--1880
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  • https://doi.org/10.1070/SM2009v200n12ABEH004062
  • https://www.mathnet.ru/eng/sm/v200/i12/p121
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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