Valery Serov & Markus Harju (2019) Born approximation for the magnetic Schrödinger operator, Inverse Problems in Science and Engineering, 27:4, 422-438, DOI: 10.1080/17415977.2018.1469626

### Born approximation for the magnetic Schrödinger operator

Saved in:
Author: Serov, Valery1; Harju, Markus1
Organizations: 1Department of Mathematical Sciences University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 1 MB)
Language: English
Published: Informa, 2019
Publish Date: 2020-04-30
Description:

# 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.

see all

Series: Inverse problems in science & engineering
ISSN: 1741-5977
ISSN-E: 1741-5985
ISSN-L: 1741-5977
Volume: 27
Issue: 4
Pages: 422 - 438
DOI: 10.1080/17415977.2018.1469626