Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/4814
Title: Golden quantum oscillator and Binet-Fibonacci calculus
Authors: Pashaev, Oktay
Nalcı, Şengül
Pashaev, Oktay
Nalcı, Şengül
Keywords: Quantum oscillators
Fibonacci sequence
Golden calculus
Issue Date: Jan-2012
Publisher: IOP Publishing Ltd.
Source: 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
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.
URI: http://doi.org/10.1088/1751-8113/45/1/015303
http://hdl.handle.net/11147/4814
ISSN: 1751-8113
1751-8113
1751-8121
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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