Abstract
The non hermiticity of the Hamiltonian is shown to be generated from the q-deformation of the algebra. As an example the q-deformed harmonic oscillator is investigated within the leading order approximation in the pseudo Hermitian perturbation theory. A generalized form of the metric is constructed. The spectrum as well as eigenstates of the system are derived explicitly.. Some applications and illustrations in q-deformed quantum statistical mechanics are also discussed.
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