Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Conference Object Citation - WoS: 1Citation - Scopus: 1Exact Quantization of Cauchy-Euler Type Forced Parametric Oscillator(IOP Publishing Ltd., 2016) Atılgan Büyükaşık, Şirin; Atılgan Büyükaşık, Şirin; Çayiç, Zehra; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyDriven and damped parametric quantum oscillator is solved by Wei-Norman Lie algebraic approach, which gives the exact form of the evolution operator. This allows us to obtain explicitly the probability densities, time-evolution of initially Glauber coherent states, expectation values and uncertainty relations. Then, as an exactly solvable model, we introduce the driven Cauchy-Euler type quantum parametric oscillator, which appears as self-adjoint quantization of the classical Cauchy-Euler differential equation. We discuss some typical behavior of this oscillator under the influence of external terms and give a concrete example.Article Citation - WoS: 30Citation - Scopus: 37Golden 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 TechnologyThe 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.