q-oscillator from the q-Hermite Polynomial
arXiv:0710.2209 · doi:10.1016/j.physletb.2008.03.043
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.
12pages, no figures. Document-class changed; q->1 limit added; refs.[9] and [10] updated. To appear in Phys. Lett. B