Inverse Scattering at a Fixed Energy for Long-Range Potentials

preprint2006arXivOpen access

Abstract

In this paper we consider the inverse scattering problem at a fixed energy for the Schrödinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading forward singularity of the scattering amplitude at some positive energy.

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