q-oscillator from the q-Hermite Polynomial

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

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• Discrete Quantum Mechanics
• Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
• Dual Christoffel transformations
• Casoratian Identities for the Wilson and Askey-Wilson Polynomials
• Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
• Une $q$-déformation de la transformation de Bargmann polyanalytique
• Perturbations around the zeros of classical orthogonal polynomials
• Exactly and quasi-exactly solvable `discrete' quantum mechanics
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• On second order q-difference equations for high-order Sobolev-type q-Hermite orthogonal polynomials