q-oscillator from the q-Hermite Polynomial

Details q-oscillator from the q-Hermite Polynomial q-oscillator from the q-Hermite Polynomial

2007-10-11

arxiv.org/abs/0710.2209v2

Phys.Lett.B663:141-145,2008

Physics

High Energy Physics

High Energy Physics - Theory

12pages, no figures. Document-class changed; q->1 limit added; refs.[9] and [10] updated. To appear in Phys. Lett. B

Scientific paper

10.1016/j.physletb.2008.03.043

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.

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