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dc.contributor.authorAktosun, Tuncay ( )
dc.contributor.authorChoque-Rivero, Abdon E. ( Orcid Icon 0000-0003-0226-9612 )
dc.contributor.authorPapanicolaou, Vassilis ( Orcid Icon 0000-0001-5405-7297 )
dc.date.accessioned2021-12-03T20:24:43Z
dc.date.available2021-12-03T20:24:43Z
dc.date.issued2019-09-30
dc.identifier.citationAktosun, T., Choque-Rivero, A. E., & Papanicolaou, V. G. (2019). Darboux transformation for the discrete Schrodinger equation. Electronic Journal of Differential Equations, 2019(112), pp. 1-34.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15006
dc.description.abstractThe discrete Schrödinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment. The Darboux transformation formulas are derived from first principles showing how the potential and the wave function change when a bound state is added to or removed from the discrete spectrum of the corresponding Schrödinger operator without changing the continuous spectrum. This is done by explicitly evaluating the change in the spectral density when a bound state is added or removed and also by determining how the continuous part of the spectral density changes. The theory presented is illustrated with some explicit examples.en_US
dc.formatText
dc.format.extent34 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDiscrete Schrödinger equationen_US
dc.subjectDarboux transformationen_US
dc.subjectSpectral densityen_US
dc.subjectSpectral functionen_US
dc.subjectGel'fand-Levitan methoden_US
dc.subjectBound statesen_US
dc.titleDarboux transformation for the discrete Schrodinger equationen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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