Abstract

We prove the existence of scattering solutions for multidimensional magnetic Schrödinger equation such that the scattered field belongs to the weighted Lebesgue space \(L_{{-}\delta}^2(\mathbb{R}^n)~(n \ge 2)\) with some \(\delta > \frac{1}{2}\). As a consequence of this we provide the mathematical foundation of the direct Born approximation for the magnetic Schrödinger operator. Connection to the inverse Born approximation is discussed with numerical examples illustrating the applicability of the method.