Publication
Multidimensional fractional Schrödinger equation
| dc.contributor.author | Rodrigues, M. M. | |
| dc.contributor.author | Vieira, Nelson | |
| dc.date.accessioned | 2025-11-10T18:53:48Z | |
| dc.date.available | 2025-11-10T18:53:48Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | This work is intended to investigate the multi-dimensional space-time fractional Schrödinger equation of the form ħ𝛻 , with ħ the Planck's constant divided by 2π, m is the mass and u(t,x) is a wave function of the particle. Here 𝛻 are operators of the Caputo fractional derivatives, where α ∈]0,1] and β ∈]1,2]. The wave function is obtained using Laplace and Fourier transforms methods and a symbolic operational form of solutions in terms of the Mittag-Leffler functions is exhibited. It is presented an expression for the wave function and for the quantum mechanical probability density. Using Banach fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations. | eng |
| dc.description.sponsorship | The work of both 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.doi | 10.1063/1.4765579 | |
| dc.identifier.issn | 0094-243X | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/14580 | |
| dc.language.iso | eng | |
| dc.peerreviewed | n/a | |
| dc.publisher | AIP | |
| dc.relation | Strategic Project - UI 4106 - 2011-2012 | |
| dc.relation.hasversion | https://pubs.aip.org/aip/acp/article-abstract/1493/1/798/852276/Multidimensional-fractional-Schrodinger-equation?redirectedFrom=fulltext | |
| dc.relation.ispartof | AIP Conference Proceedings | |
| dc.rights.uri | N/A | |
| dc.subject | Fractional partial differential equations | |
| dc.subject | Radial Fourier transform | |
| dc.subject | Mittag-Leffler function | |
| dc.subject | Time-dependent Schrödinger equation | |
| dc.subject | Fixed-point theorem | |
| dc.title | Multidimensional fractional Schrödinger equation | eng |
| dc.type | conference paper | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Strategic Project - UI 4106 - 2011-2012 | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6820 - DCRRNI ID/PEst-C%2FMAT%2FUI4106%2F2011/PT | |
| oaire.citation.conferenceDate | 2012-07-10 | |
| oaire.citation.conferencePlace | Vienna, Austria | |
| oaire.citation.endPage | 804 | |
| oaire.citation.issue | 1 | |
| oaire.citation.startPage | 798 | |
| oaire.citation.title | 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 | |
| oaire.citation.volume | 1493 | |
| oaire.fundingStream | 6820 - DCRRNI ID | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Vieira | |
| person.givenName | Nelson | |
| person.identifier.ciencia-id | 9418-DDFB-DE9D | |
| person.identifier.orcid | 0000-0001-8756-4893 | |
| person.identifier.rid | H-9130-2013 | |
| person.identifier.scopus-author-id | 55576073000 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
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