Characterization of the ranges of wave operators for Schrodinger equations with time-dependent short-range potentials via wave packet transform

Abstract: In this paper, we give a characterization of the ranges of the wave operators for Schrodinger equations with time-dependent short-range potentials by using wave packet transform. We also give an alternative proof of the existence of the wave operators for time-dependent potentials and the asymptotic completeness for timeindependent potentials.