High-Velocity Estimates and Inverse Scattering for Quantum N-Body Systems with Stark Effect

TL;DR

This paper develops a method to uniquely reconstruct pair potentials in quantum N-body systems with Stark effect using high-velocity inverse scattering, providing a reconstruction formula with an error estimate.

Contribution

It introduces a novel inverse scattering approach for quantum N-body systems with Stark effect, covering both short-range and long-range potentials.

Findings

Unique reconstruction of pair potentials from high-velocity limits.

Reconstruction formula with explicit error term.

Applicable to both short-range and long-range potentials.

Abstract

In an N-body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials and long-range potentials, from the high-velocity limit of the Dollard scattering operator. We give a reconstruction formula with an error term.