University of Oulu

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

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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)
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Language: English
Published: Informa, 2019
Publish Date: 2020-04-30


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.

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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
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
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].
Copyright information: © Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Inverse Problems in Science and Engineering Vol 27, Issue 4, available online: