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 Schrödinger equations with time-dependent "short-range" potentials by using wave packet transform, which is different from the one in Kitada-Yajima [9]. We also give an alternative proof of the existence of the wave operators for time-dependent potentials, which has been firstly proved by D. R. Yafaev [14].