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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |