Inverse scattering problem and generalized optical theorem

Abstract

We present a novel solution to the inverse scattering problem. Our solution is based on a generalization of the optical theorem, and applies directly in three dimensional space. First, we derive a necessary and sufficient condition for a half-on-shell T-matrix to be physically acceptable, which turns out to be a generalization of the optical theorem. Second, we show that the inverse scattering problem, which inquires underlying potential for a given on-shell T-matrix (scattering amplitude), can be solved by looking for a half-on-shell T-matrix that satisfies the generalized optical theorem with the given on-shell T-matrix being the boundary condition. At the end, we demonstrate that the present theory works nicely using simple systems.