Born approximation for the magnetic Schrödinger operator
Serov, Valery; Harju, Markus (2019-04-30)
Serov, Valery
Harju, Markus
Informa
30.04.2019
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
https://rightsstatements.org/vocab/InC/1.0/
© 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: http://www.tandfonline.com/10.1080/17415977.2018.1469626.
https://rightsstatements.org/vocab/InC/1.0/
© 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: http://www.tandfonline.com/10.1080/17415977.2018.1469626.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2019052717287
https://urn.fi/URN:NBN:fi-fe2019052717287
Tiivistelmä
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.
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