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Exact solution to two dimensional Dunkl harmonic oscillator in the Non-Commutative phase-space

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Abstract

In this paper, we examine the harmonic oscillator problem in non-commutative phase space (NCPS) by using the Dunkl derivative instead of the habitual one. After defining the Hamilton operator, we use the polar coordinates to derive the binding energy eigenvalue. We find eigenfunctions that correspond to these eigenvalues in terms of the Laguerre functions. We observe that the Dunkl-Harmonic Oscillator in the NCPS differs from the ordinary one in the context of providing additional information on the even and odd parities. Therefore, we conclude that working with the Dunkl operator could be more appropriate because of its rich content.

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Data Availability Statement

The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

The authors thank referee for a thorough reading of our manuscript and for constructive suggestions. This work is supported by the Internal Project, [2022/2218], of Excellent Research of the Faculty of Science of University.

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Authors and Affiliations

  1. Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia

    S. Hassanabadi, B. C. Lütfüoğlu, J. Kr̆iz̆ & H. Hassanabadi

  2. Faculty of Physics, Shahrood University of Technology, P. O. Box: 3619995161-316, Shahrood, Iran

    P. Sedaghatnia & H. Hassanabadi

  3. Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, Jinju, 660-701, Korea

    W. S. Chung

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  1. S. Hassanabadi
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Correspondence to H. Hassanabadi.

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Hassanabadi, S., Sedaghatnia, P., Chung, W.S. et al. Exact solution to two dimensional Dunkl harmonic oscillator in the Non-Commutative phase-space. Eur. Phys. J. Plus 138, 331 (2023). https://doi.org/10.1140/epjp/s13360-023-03933-2

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