Physics – Quantum Physics
Scientific paper
2010-02-02
J. Phys. A: Math. Theor. 43 (2010) 245204 (16pp)
Physics
Quantum Physics
19 pages; v2: few comments and references added; v3: small corrections, to appear in J.Phys.A
Scientific paper
10.1088/1751-8113/43/24/245204
We study the properties of sequences of the energy eigenvalues for some generalizations of q-deformed oscillators including the p,q-oscillator, the 3-, 4- and 5-parameter deformed oscillators given in the literature. It is shown that most of the considered models belong to the class of so-called Fibonacci oscillators for which any three consequtive energy levels satisfy the relation E_{n+1}=\lambda E_n+\rho E_{n-1} with real constants \lambda, \rho. On the other hand, for certain \mu-oscillator known from 1993 we prove the fact of its non-Fibonacci nature. Possible generalizations of the three-term Fibonacci relation are discussed among which we choose, as most adequate for the \mu$-oscillator, the so-called quasi-Fibonacci (or local Fibonacci) property of the energy levels. The property is encoded in the three-term quasi-Fibonacci (QF) relation with non-constant, n-dependent coefficients \lambda and \rho. Various aspects of the QF relation are elaborated for the \mu-oscillator and some of its extensions.
Gavrilik Alexandre M.
Kachurik I. I.
Rebesh Anastasiya P.
No associations
LandOfFree
Quasi-Fibonacci oscillators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quasi-Fibonacci oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi-Fibonacci oscillators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-600748