Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem
We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted fr...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/6031523 |
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| author | Lung-Hui Chen |
| author_facet | Lung-Hui Chen |
| author_sort | Lung-Hui Chen |
| collection | DOAJ |
| description | We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis. |
| format | Article |
| id | doaj-art-b7e86886c6774ecc96dd1c12ff0c8a2f |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b7e86886c6774ecc96dd1c12ff0c8a2f2025-02-03T05:49:48ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/60315236031523Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering ProblemLung-Hui Chen0Department of Mathematics, National Chung Cheng University, 168 University Rd., Min-Hsiung, Chia-Yi County 621, TaiwanWe consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis.http://dx.doi.org/10.1155/2016/6031523 |
| spellingShingle | Lung-Hui Chen Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem Advances in Mathematical Physics |
| title | Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem |
| title_full | Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem |
| title_fullStr | Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem |
| title_full_unstemmed | Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem |
| title_short | Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem |
| title_sort | remarks on the phaseless inverse uniqueness of a three dimensional schrodinger scattering problem |
| url | http://dx.doi.org/10.1155/2016/6031523 |
| work_keys_str_mv | AT lunghuichen remarksonthephaselessinverseuniquenessofathreedimensionalschrodingerscatteringproblem |