Born approximation for the magnetic Schrödinger operator

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.

KEYWORDS:

• Magnetic Schrödinger operator
• scattering
• Born approximation
• inverse problems
• numerical solution

AMS SUBJECT CLASSIFICATIONS:

• 35P25
• 35R30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Academy of Finland; Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta [application number 250215, Finnish Programme for Centres of Excellence in Research 2012–2017].