Scattering solutions and Born approximation for the magnetic Schr\"odinger operator

TL;DR

This paper establishes the existence of scattering solutions for the magnetic Schrödinger equation in multiple dimensions and introduces a direct Born approximation, with implications for inverse scattering problems.

Contribution

It proves the existence of scattering solutions in weighted Sobolev spaces and formulates the direct Born approximation for the magnetic Schrödinger operator.

Findings

Existence of scattering solutions in H^1_s space for s < -1/2

Formulation of the direct Born approximation for magnetic Schrödinger operator

Discussion of potential links to inverse scattering problems

Abstract

We prove the existence of scattering solutions for multidimensional magnetic Schr\"odinger equation which belong to the weighted Sobolev space H^1_s (R^n)(n=2,3) with some s < -1/2. As a consequence of this we formulate the direct Born approximation for the magnetic Schr\"odinger operator. Possible connections with inverse problems (inverse scattering Born approximation) are discussed.