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Mat. Sb., 2009, Volume 200, Number 12, Pages 121–156 (Mi msb7579)  

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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7579

Full text: PDF file (664 kB)
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English version:
Sbornik: Mathematics, 2009, 200:12, 1847–1880

Bibliographic databases:

UDC: 517.927
MSC: Primary 34L25, 34L40; Secondary 47E05
Received: 18.05.2009 and 08.07.2009

Citation: S. A. Stepin, A. G. Tarasov, “The resonance spectrum of a Schrödinger operator with a rapidly decaying potential”, Mat. Sb., 200:12 (2009), 121–156; Sb. Math., 200:12 (2009), 1847–1880

Citation in format AMSBIB
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\pages 1847--1880
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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. S. A. Stepin, “Asymptotic estimates for the kernel of the semigroup generated by a perturbation of the biharmonic operator by a potential”, Sb. Math., 203:6 (2012), 893–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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