Inverse scattering for a Schrödinger equation with energy dependent potential

Abstract

In this article the inverse scattering problem of reconstructing the energy dependent potential iE2−m2 P(x)+Q(x) of a Schrödinger equation on the line from its reflection coefficients and bound state data (i.e., poles of the transmission coefficients and associated norming constants) is solved using the Marchenko integral equation approach.