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One-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulation

2016-04Journal article Restricted access
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dc.contributor.authorCosta Dias, Nuno.
dc.contributor.authorJorge, Cristina.
dc.contributor.authorPrata, João Nuno.
dc.date.accessioned2025-01-10T14:37:16Z
dc.date.available2025-01-10T14:37:16Z
dc.date.issued2016-04
dc.description.abstractUsing an extension of the Hörmander product of distributions, we obtain an intrinsic formulation of one-dimensional Schrödinger operators with singular potentials. This formulation is entirely defined in terms of standard Schwartz distributions and does not require (as some previous approaches) the use of more general distributions or generalized functions. We determine, in the new formulation, the action and domain of the Schrödinger operators with arbitrary singular boundary potentials. We also consider the inverse problem, and obtain a general procedure for constructing the singular (pseudo) potential that imposes a specific set of (local) boundary conditions. This procedure is used to determine the boundary operators for the complete four-parameter family of one-dimensional Schrödinger operators with a point interaction. Finally, the δ and potentials are studied in detail, and the corresponding Schrödinger operators are shown to coincide with the norm resolvent limit of specific sequences of Schrödinger operators with regular potentialpt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationDias, N. C., Jorge, C., & Prata, J. N. (2016). One-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulation. Journal of Differential Equations, 260(8), 6548-6580.pt_PT
dc.identifier.doihttps://doi.org/10.1016/j.jde.2016.01.005pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.26/53725
dc.language.isoengpt_PT
dc.publisherElsevierpt_PT
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0022039616000061?via%3Dihubpt_PT
dc.subjectSchrödinger operatorspt_PT
dc.subjectSingular potentialspt_PT
dc.subjectPoint interactionspt_PT
dc.subjectProducts of distributionspt_PT
dc.subjectQuantum systems with boundariespt_PT
dc.titleOne-dimensional Schrödinger operators with singular potentials: A Schwartz distributional formulationpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage6580pt_PT
oaire.citation.issue8pt_PT
oaire.citation.startPage6548pt_PT
oaire.citation.titleJournal of Differential Equationspt_PT
oaire.citation.volume260pt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT

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