Quasi-Fibonacci oscillators

Abstract:
Diverse classes of non-standard deformed oscillators are explored from the viewpoint whether their energy spectra obey (or not) the familiar Fibonacci relation, whose two coefficients are some constants. The concept of quasi-Fibonacci relation/property is developed and shown to be the only possibility in the case of so-called μ-deformed or (μ;p,q)-deformed oscillators. For some other classes of deformed oscillators, three different variants of extending the Fibonacci property are proven to exist.