An asymptotic behavior of the <i>S</i>-matrix and the inverse scattering problem

Abstract

An asymptotic formula of the S-matrix as k→∞ will be shown for the general short-range scattering in RN(N≥2). The main tool for the proof is the spectral decomposition theorem for the Schrödinger operator. By the use of the asymptotic formula, the uniqueness of the inverse scattering problem will be shown and a reconstruction formula for the potential will be presented for the general short-range scattering.