The Dunkl oscillator in the momentum representation and coherent states

Abstract

Abstract We discuss quantum mechanical systems with Dunkl derivatives by constructing the Dunkl-Heisenberg relation in the momentum representation by means of the reflection operator for momentum and we obtain the corresponding position quantum eigenfunction. We examine the one-dimensional Dunkl oscillator in the momentum space in terms of ν-deformed Hermite polynomials. We obtain the energy levels as well as the ground-state and excited wave functions in terms of the ν-deformed Hermite polynomials. We also describe some properties of the ν-deformed Hermite polynomials. We apply the method to the construction of coherent states.