Dynamical Symmetries in q-deformed Quantum Mechanics

Abstract

The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction Hamiltonian in terms of the usual canonical variables. Furthermore we construct a well-defined algebra SU${}_q$(1,1) with consistent conjugation properties and comultiplication. We obtain non lowest weight representations of this algebra.

19 pages, latex, no figures

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