| Issue |
EPL
Volume 141, Number 6, March 2023
|
|
|---|---|---|
| Article Number | 60004 | |
| Number of page(s) | 7 | |
| Section | General physics | |
| DOI | https://doi.org/10.1209/0295-5075/acc352 | |
| Published online | 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: h.hasanabadi@shahroodut.ac.ir (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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