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.
Similar content being viewed by others
References
U. Aglietti and P. Santini, J. Math. Ph. 56, 062104 (2015).
A. B. Shabat, Funkts. Analiz Prilozh. 9 (3), 75 (1975).
Evg. Korotyaev, Inverse Probl. 21, 325 (2005).
A. Shabat, Theor. Math. Phys. 184, 1067 (2015).
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw Hill, New York, 1955).
A. Shabat, Theor. Math. Phys. 183, 540 (2015).
B. Levin, Lectures on Entire Functions, Translations of Mathematical Monographs, Vol. 150 (Amer. Math. Soc., Providence, RI, 1996).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.B. Shabat, 2015, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 102, No. 9, pp. 705–708.
Rights and permissions
About this article
Cite this article
Shabat, A.B. Inverse spectral problem for delta potentials. Jetp Lett. 102, 620–623 (2015). https://doi.org/10.1134/S0021364015210109
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364015210109