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

TL;DR

This paper characterizes the ranges of wave operators for Schrödinger equations with time-dependent short-range potentials using wave packet transform, providing new proofs for their existence and asymptotic completeness.

Contribution

It introduces a novel characterization of wave operator ranges via wave packet transform and offers alternative proofs for key properties in time-dependent and time-independent cases.

Findings

Characterization of wave operator ranges using wave packet transform

Alternative proof of wave operators' existence for time-dependent potentials

Proof of asymptotic completeness for time-independent potentials

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.