Inverse scattering problem in a class of nonlocal potentials. I

1987 ◽  
Vol 70 (1) ◽  
pp. 20-34 ◽  
Author(s):  
V. M. Muzafarov
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Nonlocal Potentials

scholarly journals The Inverse Scattering Problem for Static Meson Fields and Nonlocal Potentials

1975 ◽  
Vol 28 (6) ◽  
pp. 653
Author(s):  
JL Cook
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Nonlocal Potentials

The Inverse Scattering Problem for Static Meson Fields and Nonlocal Potentials

AN INVERSE SCATTERING PROBLEM FOR NONLOCAL POTENTIALS I: THE FAMILY OF PHASE EQUIVALENT WAVEFUNCTIONS

1986 ◽  
Vol 01 (07) ◽  
pp. 449-454 ◽  
Author(s):  
V.M. MUZAFAROV
Keyword(s):  
Integral Equation ◽  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
The Family ◽  
Consistent Approach ◽  
Nonlocal Potentials

We develop a consistent approach to an inverse scattering problem for the Schrodinger equation with nonlocal potentials. The main result presented in this paper is that for the two-body scattering data, given the problem of reconstructing both the family of phase equivalent two-body wavefunctions and the corresponding family of phase equivalent half-off-shell t-matrices, is reduced to solving a regular integral equation. This equation may be regarded as a generalization of the Gel’fand-Levitan equation.

AN INVERSE SCATTERING PROBLEM FOR NONLOCAL POTENTIALS II: THE FAMILY OF PHASE EQUIVALENT POTENTIALS

1987 ◽  
Vol 02 (03) ◽  
pp. 177-182 ◽  
Author(s):  
V.M. MUZAFAROV
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Algebraic Equations ◽  
Constructive Description ◽  
The Family ◽  
S Matrix ◽  
Dense Set ◽  
Rational Type ◽  
Nonlocal Potentials

Starting from the general positioning of an inverse scattering problem for the Schrodinger equation with nonlocal potentials, we give a constructive description of the family of phase equivalent two-body potentials. It is shown that if the S-matrix Sl(k) is of a rational type in k then for a dense set of potentials our main integral equation comes to a system of second-order algebraic equations, and these potentials are of a separable form. This essentially resolves all computational problems when dealing with the nuclear few-body problems.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

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