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

Aktosun, T; Papanicolaou, VG

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