Golden Quantum Oscillator and Binet-Fibonacci Calculus
Quantum Algebra
2015-05-28 v1 Mathematical Physics
math.MP
Abstract
The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases and . Quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given just by Fibonacci numbers. Ratio of successive energy levels is found as the Golden sequence and for asymptotic states it appears as the Golden ratio. This why we called this oscillator as the Golden oscillator. By double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived.
Cite
@article{arxiv.1107.4389,
title = {Golden Quantum Oscillator and Binet-Fibonacci Calculus},
author = {Oktay K. Pashaev and Sengul Nalci},
journal= {arXiv preprint arXiv:1107.4389},
year = {2015}
}
Comments
19 pages, 1 figure