2010/02/28 by A. M. Gavrilik, A M Gavrilik, I. I. Kachurik +3 · 4 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Class (philosophy) #Eigenvalues and eigenvectors #Energy (signal processing) #Fibonacci number #Property (philosophy) #Quantum Mechanics and Non-Hermitian Physics #Quasicrystal Structures and Properties #Relation (database) #cond-mat.other #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/43/24/245204
published as J. Phys. A: Math. Theor. 43 (2010) 245204 (16pp) · 19 pages; v2: few comments and references added; v3: small corrections, to appear in J.Phys.A
arxiv created 2010/05/20 · openalex publication_date 2010/05/20 · arxiv updated 2011/10/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We study the properties of the sequences of the energy eigenvalues for some generalizations of q -deformed oscillators including the p , q -oscillator, and the three-, four- and five-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 consecutive energy levels satisfy the relation E n + 1 = λ E n + ρ E n − 1 with real constants λ, ρ. On the other hand, for a certain μ-oscillator known since 1993, we prove its non-Fibonacci nature. Possible generalizations of the three-term Fibonacci relation are discussed, among which for the μ-oscillator we choose, as the most adequate, 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 the non-constant, n -dependent coefficients λ and ρ. Various aspects of the QF relation are elaborated for the μ-oscillator and some of its extensions.