Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

An extended treatment of the one-dimensional q-harmonic oscillator, based on two examples of inequivalent representations of the Heisenberg quantum algebra which appeared recently in literature is presented. The dependence of several oscillator properties such as the energy spectrum, uncertainty relations and selection rules on the new parameters characterizing those generalized representation is also discussed.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq