Stability estimate in the inverse scattering for a single quantum particle in an external short-range potential

Abstract

In this paper we consider the inverse scattering problem for the Schr{ö}dinger operator with short-range electric potential. We prove in dimension n $\ge$ 2 that the knowledge of the scattering operator determines the electric potential and we establish H{ö}lder-type stability in determining the short range electric potential.