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TMF, 2015, Volume 184, Number 2, Pages 200–211 (Mi tmf8933)  

This article is cited in 3 scientific papers (total in 3 papers)

Difference Schrödinger equation and quasisymmetric polynomials

A. B. Shabat

Landau Institute for Theoretical Physics, RAS, Moscow, Russia

Abstract: We study the singularity of solutions of the Schrödinger equation with a finite potential at the point $k=0$. In the case of delta-type potentials, we show that the nature of this singularity is automodel in a certain sense. We discuss using the obtained results to construct an approximate solution of the inverse scattering problem on the whole axis. For this, we introduce the concept of a quasisymmetric polynomial associated with a given curve.

Keywords: Schrödinger operator, Green's function, additional spectrum, difference model

DOI: https://doi.org/10.4213/tmf8933

Full text: PDF file (481 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 184:2, 1067–1077

Bibliographic databases:

Received: 18.03.2015

Citation: A. B. Shabat, “Difference Schrödinger equation and quasisymmetric polynomials”, TMF, 184:2 (2015), 200–211; Theoret. and Math. Phys., 184:2 (2015), 1067–1077

Citation in format AMSBIB
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\paper Difference Schr\"odinger equation and quasisymmetric polynomials
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\jour Theoret. and Math. Phys.
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\pages 1067--1077
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Linking options:
  • http://mi.mathnet.ru/eng/tmf8933
  • https://doi.org/10.4213/tmf8933
  • http://mi.mathnet.ru/eng/tmf/v184/i2/p200

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Shabat, “Inverse spectral problem for delta potentials”, JETP Letters, 102:9 (2015), 620–623  mathnet  crossref  crossref  isi  elib
    2. A. B. Shabat, “Constructive scattering theory”, Theoret. and Math. Phys., 193:1 (2017), 1420–1428  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. R. Ch. Kulaev, A. B. Shabat, “Some properties of Jost functions for Schrödinger equation with distribution potential”, Ufa Math. J., 9:4 (2017), 59–71  mathnet  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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