Local realizations of q-oscillators in quantum mechanics

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schrödinger type. In contrast to the standard harmonic oscillators, such systems exhibit a continuous spectrum. The general realization scheme of the q-oscillator alg...

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Bibliographic Details
Published in:Physics letters. A 1996-07, Vol.217 (1), p.7-14
Main Authors: Andrianov, A.A., Cannata, F., Dedonder, J.-P., Ioffe, M.V.
Format: Article
Language:English
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Summary:Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schrödinger type. In contrast to the standard harmonic oscillators, such systems exhibit a continuous spectrum. The general realization scheme of the q-oscillator algebra on the space of wave functions for a one-dimensional Schrödinger 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.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(96)00309-X