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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 184, Number 2, Pages 200–211
DOI: https://doi.org/10.4213/tmf8933 (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
Full-text PDF (481 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf8933
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.
Received: 18.03.2015
English version:
Theoretical and Mathematical Physics, 2015, Volume 184, Issue 2, Pages 1067–1077
DOI: https://doi.org/10.1007/s11232-015-0318-7
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://doi.org/10.4213/tmf8933
  • https://www.mathnet.ru/eng/tmf/v184/i2/p200
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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