JETP Letters

, Volume 102, Issue 9, pp 620–623 | Cite as

Inverse spectral problem for delta potentials

Methods of Theoretical Physics

Abstract

The scattering problem for the linear Schrödinger equation on the entire axis has been considered. Conditions under which the knowledge of the discrete spectrum of the Schrödinger operator is sufficient for the reconstruction of the potential have been determined. The main difference from the soliton sector is the self-similarity of the problem under consideration with respect to the extension of the spectral parameter λ. This makes it possible to reduce the inverse scattering problem to the study of the singularity of the Green’s function at λ = 0.

Keywords

Entire Function JETP Letter Discrete Spectrum Piecewise Linear Function Inverse Spectral Problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    U. Aglietti and P. Santini, J. Math. Ph. 56, 062104 (2015).CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    A. B. Shabat, Funkts. Analiz Prilozh. 9 (3), 75 (1975).MathSciNetGoogle Scholar
  3. 3.
    Evg. Korotyaev, Inverse Probl. 21, 325 (2005).CrossRefADSMathSciNetMATHGoogle Scholar
  4. 4.
    A. Shabat, Theor. Math. Phys. 184, 1067 (2015).CrossRefMathSciNetGoogle Scholar
  5. 5.
    E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw Hill, New York, 1955).MATHGoogle Scholar
  6. 6.
    A. Shabat, Theor. Math. Phys. 183, 540 (2015).CrossRefMathSciNetGoogle Scholar
  7. 7.
    B. Levin, Lectures on Entire Functions, Translations of Mathematical Monographs, Vol. 150 (Amer. Math. Soc., Providence, RI, 1996).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations