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A numerical method for the fractional Schrödinger type equation of spatial dimension two

2013-03-19Artigo científico Acesso restrito
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg03:Saúde de Qualidade
datacite.subject.sdg07:Energias Renováveis e Acessíveis
datacite.subject.sdg11:Cidades e Comunidades Sustentáveis
dc.contributor.authorFord, Neville J.
dc.contributor.authorRodrigues, M. Manuela
dc.contributor.authorVieira, Nelson
dc.date.accessioned2026-03-12T14:24:22Z
dc.date.available2026-03-12T14:24:22Z
dc.date.issued2013-03-19
dc.description.abstractThis work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrödinger type equation. In the early part of the paper, the wave function is obtained using Laplace and Fourier transform methods and a symbolic operational form of the solutions in terms of Mittag-Leffler functions is provided. We present an expression for the wave function and for the quantum mechanical probability density. We introduce a numerical method to solve the case where the space component has dimension two. Stability conditions for the numerical scheme are obtained.eng
dc.description.sponsorshipThe second and third authors were supported by FEDER funds through COMPETE–Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690.
dc.identifier.citationFord, N.J., Manuela Rodrigues, M. & Vieira, N. A numerical method for the fractional Schrödinger type equation of spatial dimension two. fcaa 16, 454–468 (2013). https://doi.org/10.2478/s13540-013-0028-5
dc.identifier.doi10.2478/s13540-013-0028-5
dc.identifier.issn1311-0454
dc.identifier.issn1314-2224
dc.identifier.urihttp://hdl.handle.net/10400.8/15851
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer
dc.relationStrategic Project - UI 4106 - 2011-2012
dc.relation.hasversionhttps://link.springer.com/article/10.2478/s13540-013-0028-5
dc.relation.ispartofFractional Calculus and Applied Analysis
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectFinite difference method
dc.subjectFractional partial differential equation
dc.subjectFractional Schrödinger equation
dc.subjectMittag-Leffler function
dc.titleA numerical method for the fractional Schrödinger type equation of spatial dimension twoeng
dc.typejournal article
dspace.entity.typePublication
oaire.awardNumberPEst-C/MAT/UI4106/2011
oaire.awardTitleStrategic Project - UI 4106 - 2011-2012
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6820 - DCRRNI ID/PEst-C%2FMAT%2FUI4106%2F2011/PT
oaire.citation.endPage468
oaire.citation.issue2
oaire.citation.startPage454
oaire.citation.titleFractional Calculus and Applied Analysis: An International Journal for Theory and Applications
oaire.citation.volume16
oaire.fundingStream6820 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameVieira
person.givenNameNelson
person.identifier.ciencia-id9418-DDFB-DE9D
person.identifier.orcid0000-0001-8756-4893
person.identifier.ridH-9130-2013
person.identifier.scopus-author-id55576073000
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
relation.isAuthorOfPublicationf530f82c-8351-4c64-a33e-4c34fe4ac22a
relation.isAuthorOfPublication.latestForDiscoveryf530f82c-8351-4c64-a33e-4c34fe4ac22a
relation.isProjectOfPublication9f37d183-d2e8-4bfb-856f-47ce40c20898
relation.isProjectOfPublication.latestForDiscovery9f37d183-d2e8-4bfb-856f-47ce40c20898

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