Quantum inverse scattering for time-decaying harmonic oscillators

TL;DR

This paper investigates the inverse scattering problem for a multidimensional quantum system with a time-decaying harmonic oscillator, proving that the scattering operator uniquely determines the potential functions using the Enss--Weder method.

Contribution

It extends inverse scattering theory to time-decaying harmonic oscillators with short-range potentials, establishing uniqueness results.

Findings

Scattering operator uniquely determines potential functions.

Application of Enss--Weder time-dependent method to this system.

Analysis of multidimensional quantum scattering with time decay.

Abstract

Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inverse scatterings in this two-body quantum system perturbed by short-range potential functions that have a bounded part and a locally singular part. Applying the Enss--Weder time-dependent method, we prove that the scattering operator determines the potential functions uniquely.