English

Hermite polynomials and Fibonacci Oscillators

Statistical Mechanics 2019-01-30 v2 High Energy Physics - Theory Quantum Physics

Abstract

We compute the (q1,q2q_1,q_2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1,q2q_1, q_2)-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 q1=1q_1 = 1 and q21q_2\to1 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

R2 v1 2026-06-23T01:48:54.363Z