Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations

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dc.contributorVirginia Techen
dc.contributor.authorAktosun, Tuncayen
dc.contributor.authorKlaus, Martinen
dc.contributor.authorvan der Mee, Cornelisen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:19Zen
dc.date.available2014-04-09T18:12:19Zen
dc.date.issued1996-12en
dc.description.abstractThe one-dimensional Schrodinger equation and two of its generalizations are considered, as they arise in quantum mechanics, wave propagation in a nonhomogeneous medium, and wave propagation in a nonconservative medium where energy may be absorbed or generated. Generically, the zero-energy transmission coefficient vanishes when the potential is nontrivial, but in the exceptional case this coefficient is nonzero, resulting in tunneling through the potential. It is shown that any nontrivial exceptional potential can always be fragmented into two generic pieces. Furthermore, any nontrivial potential, generic or exceptional, can be fragmented into generic pieces in infinitely many ways. The results remain valid when Dirac delta functions are included in the potential and other coefficients are added to the Schrodinger equation. For such Schrodinger equations, factorization formulas are obtained that relate the scattering matrices of the fragments to the scattering matrix of the full problem. (C) 1996 American Institute of Physics.en
dc.description.sponsorshipNSF DMS-9501053en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationAktosun, T.; Klaus, M.; vanderMee, C., "Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations," J. Math. Phys. 37, 5897 (1996); http://dx.doi.org/10.1063/1.531754en
dc.identifier.doihttps://doi.org/10.1063/1.531754en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47046en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/37/12/10.1063/1.531754en
dc.language.isoenen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectinverse scatteringen
dc.subjectwave scatteringen
dc.titleFactorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equationsen
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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