On multidimensional inverse scattering under the Stark effect

TL;DR

This paper advances the understanding of multidimensional inverse scattering for quantum systems under a constant electric field by proposing simplified methods to sharpen key estimates, enabling unique determination of short-range potentials.

Contribution

It introduces new, simpler techniques for sharpening estimates in inverse scattering analysis, facilitating the unique identification of short-range potentials in quantum systems under the Stark effect.

Findings

Methods provide sharper estimates for inverse scattering problems.

Unique determination of short-range potentials from scattering operators.

Simplification of analysis compared to previous approaches.

Abstract

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening key estimates in the analysis, which are much simpler than those in the previous works. Our methods give an appropriate class of short-range potentials which can be determined uniquely by scattering operators, that seems natural in terms of direct scattering problems.