Abstract
Reconstruction of the Schrödinger-equation potential (for the case of s-scattering) from scattering data by the Krein method is discussed. Analytically, the problem reduces to the solution of a system of linear inhomogeneous algebraic equations for certain functions. The Bargmann potentials, determined earlier by other methods, are shown to result from the solution of the problem for various particular cases.
Similar content being viewed by others
References
V. Bargmann, Rev. Mod. Phys.,21, 488, 1949.
M. Blažek, Czech. J. Phys.,B12, 249, 258, 1962.
I. M. Gel'fand and B. M. Levitan, Izv. AN SSSR, ser. matem.,15, 309, 1951.
Z. S. Agranovich and V. A. Marchenko, The Inverse Problem of the Quantum Theory of Scattering [in Russian], Izd-vo Khar'kovskogo universiteta, 1959.
M. G. Krein, DAN SSSR,97, 21, 1954.
M. G. Krein, DAN SSSR,105, 433, 1955.
M. G. Krein, DAN SSSR,111, 1167, 1956.
M. G. Krein, Spectral and Transition Functions of One-Dimensional Boundary-Value Problems; Lectures Delivered at Moscow State University [in Russian], 1956.
L. D. Fadeev, UMN14, 57, 1959.
M. Blažek, Czech. J. Phys.,B12, 497, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Poplavskii, I.V. Reconstruction of the Schrödinger-equation potential from scattering data by the Krein method. Soviet Physics Journal 11, 8–13 (1968). https://doi.org/10.1007/BF00817936
Issue Date:
DOI: https://doi.org/10.1007/BF00817936