WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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Institution Author: search.filters.institutionAuthor.Nalcı, ŞengülSubject: search.filters.subject.Fibonacci sequence

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  • Article
    Citation - WoS: 30
    Citation - Scopus: 37
    Golden quantum oscillator and Binet-Fibonacci calculus
    (IOP Publishing Ltd., 2012) Pashaev, Oktay; Nalcı, Şengül; Pashaev, Oktay; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.