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dc.contributor.authorPashaev, Oktay
dc.contributor.authorNalcı, Şengül
dc.date.accessioned2017-02-09T07:04:56Z
dc.date.available2017-02-09T07:04:56Z
dc.date.issued2012-01
dc.identifier.citationPashaev, O., and Nalcı, Ş. (2012). Golden quantum oscillator and Binet-Fibonacci calculus. Journal of Physics A: Mathematical and Theoretical, 45(1). doi:10.1088/1751-8113/45/1/015303en_US
dc.identifier.issn1751-8113
dc.identifier.urihttp://doi.org/10.1088/1751-8113/45/1/015303
dc.identifier.urihttp://hdl.handle.net/11147/4814
dc.description.abstractThe Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = and Q = 1/, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated.en_US
dc.description.sponsorshipTUBITAK, TBAG Project 110T679 and the Izmir Institute of Technologyen_US
dc.language.isoengen_US
dc.publisherIOP Publishingen_US
dc.relationinfo:eu-repo/grantAgreement/TUBITAK/TBAG/110T679en_US
dc.relation.isversionof10.1088/1751-8113/45/1/015303en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectQuantum oscillatorsen_US
dc.subjectFibonacci sequenceen_US
dc.subjectGolden calculusen_US
dc.titleGolden quantum oscillator and Binet-Fibonacci calculusen_US
dc.typearticleen_US
dc.contributor.authorIDTR57865en_US
dc.contributor.authorIDTR57807en_US
dc.contributor.institutionauthorPashaev, Oktay
dc.contributor.institutionauthorNalcı, Şengül
dc.relation.journalJournal of Physics A: Mathematical and Theoreticalen_US
dc.contributor.departmentİYTE, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume45en_US
dc.identifier.issue1en_US
dc.identifier.wosWOS:000298146200014
dc.identifier.scopusSCOPUS:2-s2.0-83455206913
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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