Long-range Scattering Matrix for Schr\"odinger-type Operators

TL;DR

This paper demonstrates that the scattering matrix for certain Schr"odinger-type operators with long-range perturbations can be characterized as a Fourier integral operator, linking quantum scattering to classical scattering maps.

Contribution

It establishes that the scattering matrix is a Fourier integral operator with a phase function related to the classical scattering map for long-range Schr"odinger operators.

Findings

Scattering matrix is a Fourier integral operator.

Phase function corresponds to the generating function of the classical scattering map.

Results connect quantum and classical scattering theories.

Abstract

We show that the scattering matrix for a class of Schr\"odinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the generating function of the modified classical scattering map.