Volume 141, Number 6, March 2023
|Number of page(s)
|24 March 2023
The Dunkl oscillator in the momentum representation and coherent states
1 Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University - Jinju 660-701, Korea
2 Faculté Saint-Jean, University of Alberta - Edmonton, AB T6C 4G9, Canada
3 Faculty of Physics, Shahrood University of Technology - Shahrood, Iran
(a) E-mail: firstname.lastname@example.org (corresponding author)
Received: 6 April 2022
Accepted: 10 March 2023
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.
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