# Inverse scattering for a Schrödinger equation with energy dependent potential

@article{Mee2001InverseSF,
title={Inverse scattering for a Schr{\"o}dinger equation with energy dependent potential},
author={Cornelis Van der Mee and Vjacheslav Pivovarchik},
journal={Journal of Mathematical Physics},
year={2001},
volume={42},
pages={158-181}
}
• Published 3 January 2001
• Mathematics
• Journal of Mathematical Physics
In this article the inverse scattering problem of reconstructing the energy dependent potential iE2−m2 P(x)+Q(x) of a Schrodinger 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.
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Wave scattering is analyzed in a one-dimensional nonconservative medium governed by the generalized Schrodinger equation d2ψ/dx2+k2ψ=[ikP(x)+Q(x)]ψ, where P(x) and Q(x) are real, integrable
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