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Wave scattering in one dimension with absorption

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dc.contributorVirginia Techen
dc.contributor.authorAktosun, T.en
dc.contributor.authorKlaus, Martinen
dc.contributor.authorvan der Mee, Cornelisen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:29Zen
dc.date.available2014-04-09T18:12:29Zen
dc.date.issued1998-04en
dc.description.abstractWave scattering is analyzed in a one-dimensional nonconservative medium governed by the generalized Schrodinger equation d(2) psi/dx(2)+k(2) psi=[ikP(x)+Q(x)]psi, where P(x) and Q(x) are real, integrable potentials with finite first moments. Various properties of the scattering solutions are obtained. The corresponding scattering matrix is analyzed, and its small-k and large-k asymptotics are established. The bound states, which correspond to the poles of the transmission coefficient in the upper-half complex plane, are studied in detail. When the medium is not purely absorptive, i.e., unless P(x)less than or equal to 0, it is shown that there may be bound states at complex energies, degenerate bound states, and singularities of the transmission coefficient imbedded in the continuous spectrum. Some explicit examples are provided illustrating the theory. (C) 1998 American Institute of Physics. [S0022-2488(98)01503-5].en
dc.description.sponsorshipNSF DMS-9501053en
dc.description.sponsorshipCNR-GNFMen
dc.description.sponsorshipMURSTen
dc.identifier.citationAktosun, T.; Klaus, M.; van der Mee, C., "Wave scattering in one dimension with absorption," J. Math. Phys. 39, 1957 (1998); http://dx.doi.org/10.1063/1.532271en
dc.identifier.doihttps://doi.org/10.1063/1.532271en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47099en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/39/4/10.1063/1.532271en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectinverse scatteringen
dc.subjectequationen
dc.subjectenergyen
dc.subjectlineen
dc.titleWave scattering in one dimension with absorptionen
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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