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Recovery of a potential from the ratio of reflection and transmission coefficients

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dc.contributor.author Aktosun, T en
dc.contributor.author Papanicolaou, VG en
dc.date.accessioned 2014-03-01T01:19:29Z
dc.date.available 2014-03-01T01:19:29Z
dc.date.issued 2003 en
dc.identifier.issn 0022-2488 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/15521
dc.subject Bound States en
dc.subject Data Consistency en
dc.subject Inverse Scattering en
dc.subject schrodinger equation en
dc.subject Transmission Coefficient en
dc.subject.classification Physics, Mathematical en
dc.subject.other INVERSE SCATTERING en
dc.subject.other SCHRODINGER-EQUATION en
dc.subject.other LINE en
dc.title Recovery of a potential from the ratio of reflection and transmission coefficients en
heal.type journalArticle en
heal.identifier.primary 10.1063/1.1614871 en
heal.identifier.secondary http://dx.doi.org/10.1063/1.1614871 en
heal.language English en
heal.publicationDate 2003 en
heal.abstract For the one-dimensional Schrodinger equation, the analysis is provided to recover the potential from the data consisting of the ratio of a reflection coefficient to the transmission coefficient. It is investigated whether such data uniquely constructs a reflection coefficient, the number of bound states, bound-state energies, bound-state norming constants, and a corresponding potential. In all three cases when there is no knowledge of the support of the potential, the support of the potential is confined to a half-line, and the support is confined to a finite interval, various uniqueness and nonuniqueness results are established, the precise criteria are provided for the uniqueness and the nonuniqueness and the degree of nonuniqueness, and the recovery is illustrated with some explicit examples. (C) 2003 American Institute of Physics. en
heal.publisher AMER INST PHYSICS en
heal.journalName Journal of Mathematical Physics en
dc.identifier.doi 10.1063/1.1614871 en
dc.identifier.isi ISI:000186094300001 en
dc.identifier.volume 44 en
dc.identifier.issue 11 en
dc.identifier.spage 4875 en
dc.identifier.epage 4883 en


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