Spectral properties of the Kronig-Penney Hamiltonian with a localized impurity

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dc.contributorVirginia Techen
dc.contributor.authorFassari, S.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-03-20en
dc.date.accessioned2014-04-09T18:12:27Zen
dc.date.available2014-04-09T18:12:27Zen
dc.date.issued1989-06en
dc.description.abstractIt is shown that there exist bound states of the operator H ±λ=−(d 2/d x 2) +∑ m∈Z δ(⋅−(2m+1)π)±λW, W being an L 1(−∞,+∞) non‐negative function, in every sufficiently far gap of the spectrum of H 0=−d 2/d x 2 +∑ m∈Z δ(⋅−(2m+1)π). Such an operator represents the Schrödinger Hamiltonian of a Kronig–Penney‐type crystal with a localized impurity. The analyticity of the greatest (resp. lowest) eigenvalue of H λ (resp. H −λ) occurring in a spectral gap as a function of the coupling constant λ when W is assumed to have an exponential decay is also proven.en
dc.description.sponsorshipDepartment of Energy De-FG05-87ER25033en
dc.description.sponsorshipNSF DMS-8701050en
dc.identifier.citationFassari, S., "Spectral properties of the Kronig-Penney Hamiltonian with a localized impurity," J. Math. Phys. 30, 1385 (1989); http://dx.doi.org/10.1063/1.528320en
dc.identifier.doihttps://doi.org/10.1063/1.528320en
dc.identifier.issn0022-2488en
dc.identifier.urihttp://hdl.handle.net/10919/47085en
dc.identifier.urlhttp://scitation.aip.org/content/aip/journal/jmp/30/6/10.1063/1.528320en
dc.language.isoen_USen
dc.publisherAIP Publishingen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectbound statesen
dc.subjecteigenvaluesen
dc.subjectspectral propertiesen
dc.titleSpectral properties of the Kronig-Penney Hamiltonian with a localized impurityen
dc.title.serialJournal of Mathematical Physicsen
dc.typeArticle - Refereeden

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