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arXiv · hep-th/9604145

Local realizations of $q$-Oscillators in Quantum Mechanics

A. A. Andrianov·F. Cannata·J. -P. Dedonder·M. V. Ioffe
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Abstract

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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A. A. Andrianov, F. Cannata, J. -P. Dedonder, M. V. Ioffe. 1996-04-23. Local realizations of $q$-Oscillators in Quantum Mechanics. https://doi.org/10.1016/0375-9601(96)00309-x

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