An Inverse Scattering Problem

Abstract

In this paper we give an elementary method to study an inverse scattering problem for a pair of Hamiltonians (H(h), H0(h)) on L2(IRn), where H0(h) = - h2 ∆, H(h) = H0(h) + V, and V is a short-range potential. We show that, in dimension , the scattering operators which are localized near a fixed energy ,determine the asymptotic of the potential V at infinity. This approach can be used to solve an inverse scattering problem for isotropic external metrics.