Hermite polynomials and Fibonacci Oscillators
Statistical Mechanics
2019-01-30 v2 High Energy Physics - Theory
Quantum Physics
Abstract
We compute the ()-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the ()-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states. We conjecture that this achievement may find applications in the inclusion of disorder and impurity in quantum systems. The ordinary quantum mechanics is easily recovered as and or vice versa.
Keywords
Cite
@article{arxiv.1805.03229,
title = {Hermite polynomials and Fibonacci Oscillators},
author = {Andre A. Marinho and Francisco A. Brito},
journal= {arXiv preprint arXiv:1805.03229},
year = {2019}
}
Comments
15 pages, 4 figures; version to appear in Journal of Mathematical Physics