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.