拟Fibonacci振子
Quasi-Fibonacci oscillators
摘要：
本文研究了文献中给出的几种q变形振子的推广形式，包括p，q变形振子，3参数，4参数和5参数变形振子的能量本征值序列的性质.结果表明，大多数模型属于Fibonacci振子类，其任意三个连续能级满足关系式E_{n+1} =λE_n+ρ E_{n-1}，其中λ，ρ为实常数.另一方面，对于1993年已知的μ振子，我们证明了它的非Fibonacci性质。讨论了三项Fibonacci关系的可能的推广，其中我们选择了能级的所谓准Fibonacci（或局部Fibonacci）性质作为最适合μ-振子的性质。该性质被编码在三项准斐波那契（QF）关系中，具有非常数，n相关系数λ和ρ。对于μ振荡器及其某些扩展，详细阐述了QF关系的各个方面.
英文摘要：
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}=λE_n+ρE_{n-1} with real constants λ, ρ. On the other hand, for certain μ-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 μ$-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 λand ρ. Various aspects of the QF relation are elaborated for the μ-oscillator and some of its extensions.
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