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Europhysics Letters (EPL)

The Dunkl oscillator in the momentum representation and coherent states

Won Sang Chung, M. de Montigny, HASSAN HASSANABADI

Published Mar 1, 2023• 10 citations
Publisher

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.

DOI
10.1209/0295-5075/acc352

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