Golden quantum oscillator and Binet-Fibonacci calculus
| dc.contributor.author | Pashaev, Oktay | |
| dc.contributor.author | Nalcı, Şengül | |
| dc.coverage.doi | 10.1088/1751-8113/45/1/015303 | |
| dc.date.accessioned | 2017-02-09T07:04:56Z | |
| dc.date.available | 2017-02-09T07:04:56Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | The 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.sponsorship | TUBITAK, TBAG Project 110T679 and the Izmir Institute of Technology | en_US |
| dc.identifier.citation | Pashaev, O., and Nalcı, Ş. (2012). Golden quantum oscillator and Binet-Fibonacci calculus. Journal of Physics A: Mathematical and Theoretical, 45(1). doi:10.1088/1751-8113/45/1/015303 | en_US |
| dc.identifier.doi | 10.1088/1751-8113/45/1/015303 | |
| dc.identifier.doi | 10.1088/1751-8113/45/1/015303 | en_US |
| dc.identifier.issn | 1751-8113 | |
| dc.identifier.issn | 1751-8121 | |
| dc.identifier.issn | 1751-8113 | |
| dc.identifier.scopus | 2-s2.0-83455206913 | |
| dc.identifier.uri | http://doi.org/10.1088/1751-8113/45/1/015303 | |
| dc.identifier.uri | https://hdl.handle.net/11147/4814 | |
| dc.language.iso | en | en_US |
| dc.publisher | IOP Publishing Ltd. | en_US |
| dc.relation | info:eu-repo/grantAgreement/TUBITAK/TBAG/110T679 | en_US |
| dc.relation.ispartof | Journal of Physics A: Mathematical and Theoretical | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Quantum oscillators | en_US |
| dc.subject | Fibonacci sequence | en_US |
| dc.subject | Golden calculus | en_US |
| dc.title | Golden quantum oscillator and Binet-Fibonacci calculus | en_US |
| dc.type | Article | en_US |
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| gdc.author.institutional | Pashaev, Oktay | |
| gdc.author.institutional | Nalcı, Şengül | |
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| gdc.description.department | İzmir Institute of Technology. Mathematics | en_US |
| gdc.description.issue | 1 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
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| gdc.description.volume | 45 | en_US |
| gdc.description.wosquality | Q2 | |
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| gdc.oaire.keywords | Golden calculus | |
| gdc.oaire.keywords | Mathematics - Quantum Algebra | |
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| gdc.oaire.keywords | Fibonacci sequence | |
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| gdc.oaire.keywords | Quantum oscillators | |
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