Explicit inverse scattering for the one-dimensional Schrödinger equation.
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| Title: | Explicit inverse scattering for the one-dimensional Schrödinger equation. |
|---|---|
| Authors: | Gibson, Peter C.1 (AUTHOR) pcgibson@yorku.ca |
| Source: | Mathematical Models & Methods in Applied Sciences. Apr2026, Vol. 36 Issue 4, p751-785. 35p. |
| Subjects: | Schrödinger equation, Inverse scattering transform, Acoustic imaging, Schroedinger, Erwin, 1887-1961, Electric impedance, Numerical calculations, Quantum scattering, Scattering (Mathematics) |
| Abstract: | Working with the one-dimensional Schrödinger equation in impedance form, we derive an exact inverse scattering formula that expresses impedance in terms of the reflection coefficient, and we prove injectivity of the scattering map for impedance functions of lower regularity than previously analyzed. The inverse scattering formula translates directly into an efficient numerical algorithm that accurately transforms digital scattering data into impedance. The results apply to acoustic imaging of layered media, as well as to inverse quantum scattering. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192085589 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Explicit inverse scattering for the one-dimensional Schrödinger equation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gibson%2C+Peter+C%2E%22">Gibson, Peter C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pcgibson@yorku.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Models+%26+Methods+in+Applied+Sciences%22">Mathematical Models & Methods in Applied Sciences</searchLink>. Apr2026, Vol. 36 Issue 4, p751-785. 35p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Schrödinger+equation%22">Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+scattering+transform%22">Inverse scattering transform</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustic+imaging%22">Acoustic imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Schroedinger%2C+Erwin%2C+1887-1961%22">Schroedinger, Erwin, 1887-1961</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+impedance%22">Electric impedance</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+calculations%22">Numerical calculations</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+scattering%22">Quantum scattering</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Mathematics%29%22">Scattering (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Working with the one-dimensional Schrödinger equation in impedance form, we derive an exact inverse scattering formula that expresses impedance in terms of the reflection coefficient, and we prove injectivity of the scattering map for impedance functions of lower regularity than previously analyzed. The inverse scattering formula translates directly into an efficient numerical algorithm that accurately transforms digital scattering data into impedance. The results apply to acoustic imaging of layered media, as well as to inverse quantum scattering. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Models & Methods in Applied Sciences is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0218202526500132 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 751 Subjects: – SubjectFull: Schrödinger equation Type: general – SubjectFull: Inverse scattering transform Type: general – SubjectFull: Acoustic imaging Type: general – SubjectFull: Schroedinger, Erwin, 1887-1961 Type: general – SubjectFull: Electric impedance Type: general – SubjectFull: Numerical calculations Type: general – SubjectFull: Quantum scattering Type: general – SubjectFull: Scattering (Mathematics) Type: general Titles: – TitleFull: Explicit inverse scattering for the one-dimensional Schrödinger equation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gibson, Peter C. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02182025 Numbering: – Type: volume Value: 36 – Type: issue Value: 4 Titles: – TitleFull: Mathematical Models & Methods in Applied Sciences Type: main |
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