The Dunkl oscillator in the momentum representation and coherent states
- 1 March 2023
- journal article
- research article
- Published by IOP Publishing in Europhysics Letters
- Vol. 141 (6), 60004
- https://doi.org/10.1209/0295-5075/acc352
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 nu-deformed Hermite polynomials. We obtain the energy levels as well as the ground-state and excited wave functions in terms of the nu-deformed Hermite polynomials. We also describe some properties of the nu-deformed Hermite polynomials. We apply the method to the construction of coherent states. Copyright (c) 2023 EPLAKeywords
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