This paper presents explicit solutions of the Marchenko equation relevant to the solution of the inverse scattering problem of determining the real potential Q(x) in the 1-D Schroedinger equation on the line frpm the reflection coefficient R(k), which is assumed to be rational. The reflection coefficient is written in the form iC(k-iA)^{-1}B. State space methods are applied to solve the Marchenko equation, both without and with bound states.
Exact solution of the Marchenko equation relevant to inverse scattering on the line
VAN DER MEE, CORNELIS VICTOR MARIA
2000-01-01
Abstract
This paper presents explicit solutions of the Marchenko equation relevant to the solution of the inverse scattering problem of determining the real potential Q(x) in the 1-D Schroedinger equation on the line frpm the reflection coefficient R(k), which is assumed to be rational. The reflection coefficient is written in the form iC(k-iA)^{-1}B. State space methods are applied to solve the Marchenko equation, both without and with bound states.
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