q-oscillator from the q-Hermite Polynomial
High Energy Physics - Theory
2008-11-26 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-oscillator is derived from the exact Heisenberg operator solution. Now the q-oscillator stands on the equal footing to the ordinary harmonic oscillator.
Cite
@article{arxiv.0710.2209,
title = {q-oscillator from the q-Hermite Polynomial},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0710.2209},
year = {2008}
}
Comments
12pages, no figures. Document-class changed; q->1 limit added; refs.[9] and [10] updated. To appear in Phys. Lett. B