Gauge equivalence and inverse scattering for long-range magnetic potentials

TL;DR

This paper establishes a one-to-one correspondence between gauge equivalence classes of Schrödinger operators with long-range magnetic potentials and their scattering matrices in exterior domains, advancing inverse scattering theory.

Contribution

It proves the unique correspondence between gauge classes of Hamiltonians and S-matrices for long-range magnetic potentials in exterior domains with convex obstacles.

Findings

One-to-one correspondence between gauge classes and S-matrices.

Extension of inverse scattering results to long-range magnetic potentials.

Applicability to exterior domains with convex obstacles.

Abstract

For Schroedinger operators with long-range magnetic vector potentials and short-range electric scalar potentials in an exterior domain $\Omega$ in ${\bf R}^n$ with $n \geq 2$, we show that there is a one-to-one correspondence between the gauge equivalent classes of Hamiltonians and those of S-matrices if $\Omega$ is exterior to a bounded convex obstacle.