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Journal of Physics A Mathematical and General

A q-deformed harmonic oscillator in a finite-dimensional Hilbert space

Le‐Man Kuang

Published Oct 21, 1993• 11 citations
Publisher

Abstract

A q-deformed harmonic oscillator (q-HO) in a finite-dimensional Hilbert space (FDHS) is presented. Some basic characteristics of the q-HO in the FDHS is discussed. It is found that the quantum algebra su q (1,1) can be realized in terms of the q-HO in the FDHS on the root of unit.
DOI
10.1088/0305-4470/26/20/004

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The possibility of q-deformation of known exactly solvable quantum mechanical models is considered via the dynamical symmetry of the radial problem. The algebraic structure of the D-dimensional simple harmonic oscillator is analysed from this point of view. In the two-dimensional case, q-deformed bosons are introduced for the radial degrees of freedom, which together with the standard angular operators yield the so(2)(+)so q (2,1) dynamical algebra. The corresponding Hilbert space is identified and possible q-deformed Hamiltonians described.