Local realizations of $q$-Oscillators in Quantum Mechanics

Details Local realizations of $q$-Oscillators in Quantum Mechanics Local realizations of $q$-Oscillators in Quantum Mechanics

1996-04-23

arxiv.org/abs/hep-th/9604145v1

Phys.Lett. A217 (1996) 7

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTeX, Phys. Lett. A, to be published

Scientific paper

10.1016/0375-9601(96)00309-X

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous spectrum. The general scheme of realization of the q-oscillator algebra on the space of wave functions for a one-dimensional Schroedinger Hamiltonian shows the existence of non-Fock irreducible representations associated to the continuous part of the spectrum and directly related to the deformation. An algorithm for the mapping of energy levels is described.

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