Research PapersNo Access

Effect of the Wigner–Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

S. Sargolzaeipor

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

E-mail Address: [email protected]

Corresponding author

Search for more papers by this author

H. Hassanabadi

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

Search for more papers by this author

, and

W. S. Chung

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

Search for more papers by this author

https://doi.org/10.1142/S0217732318501468Cited by:25 (Source: Crossref)

Abstract

In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner–Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue equation and the corresponding wave function for Dirac harmonic oscillator and Dirac equation, respectively. It is shown all results in the limit state satisfied what we had expected before.

Keywords:

PACS: 03.65.Ge, 03.65.Fd, 02.30.Gp

References

1. M. Jimbo, Lett. Math. Phys. 11, 247 (1986). Crossref, Web of Science, ADS, Google Scholar
2. V. G. Drinfeld, in Proc. Int. Congress of Mathematicians, Berkeley, 1986, ed. A. M. Gleason (American Mathematical Society, Providence, 1987). Google Scholar
3. M. Arik and D. Coon, J. Math. Phys. 17, 524 (1976). Crossref, Web of Science, ADS, Google Scholar
4. A. J. Macfarlane, J. Phys. A 22, 4581 (1989). Crossref, ADS, Google Scholar
5. L. Biedenharn, J. Phys. A 22, L873 (1989). Crossref, ADS, Google Scholar
6. M. Moshinsky and A. Szczepaniak, J. Phys. A: Math. Gen. 22, L817 (1989). Crossref, ADS, Google Scholar
7. J. N. Ginocchio, Phys. Rep. 414, 165 (2005). Crossref, Web of Science, ADS, Google Scholar
8. J. N. Ginocchio and A. Leviatan, Phys. Lett. B 425, 1 (1998). Crossref, Web of Science, ADS, Google Scholar
9. N. Hatami and M. R. Setare, Phys. Lett. A, https://doi.org/10.1016/j.physleta.2016.08.049 (2016). Google Scholar
10. A. Boumali and H. Hassanabadi, Adv. High Energy Phys., https://doi.org/10.1155/2017/9371391 (2017). Google Scholar
11. V. X. Genest, L. Vinet and A. Zhedanov, J. Phys. Conf. Ser. 512, 012010 (2014). Crossref, Google Scholar
12. V. X. Genest, M. E. H. Ismail, L. Vinet and A. Zhedanov, Commun. Math. Phys., https://doi.org/10.1007/s00220-014-1915-2, to appear (2013). Google Scholar
13. V. X. Genest, L. Vinet, and A. Zhedanov, SIGMA 9, 18 (2013). Google Scholar
14. V. X. Genest, M. E. H. Ismail, L. Vinet and A. Zhedanov, J. Phys. A: Math. Theor. 46, 145201 (2013). Crossref, Web of Science, ADS, Google Scholar
15. E. Wigner, Phys. Rev. 77, 711 (1950). Crossref, Web of Science, ADS, Google Scholar
16. C. Dunkl, T. Am. Math. Soc. 311, 167 (1989). Crossref, Web of Science, Google Scholar
17. C. Dunkl, Math. Z. 197, 33 (1988). Crossref, Web of Science, Google Scholar
18. (Eds.) L. Vinet and J. F. Van Diejen, Calogero-Mosersutherland Models (Springer, 2000). Google Scholar
19. G. J. Heckman, Prog. Math. 101, 181 (1991). Crossref, Google Scholar
20. F. Dai and Y. Xu, Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer, 2013). Crossref, Google Scholar
21. J. J. Sakurai, Modern Quantum Mechanics, ISBN 0-201-53929-2 (1994). Google Scholar
22. L. Yang, Phys. Rev. 84, 788 (1951). Crossref, Web of Science, ADS, Google Scholar
23. W. S. Chung and H. Hassanabadi, Int. J. Geom. Methods Mod. Phys., https://doi.org/10.1142/S0219887818501232 (2018). Google Scholar
24. S. Sargolzaeipor, H. Hassanabadi and W. S. Chung, Can. J. Phys., https://doi.org/10.1139/cjp-2016-0875 (2017). Google Scholar
25. A. Boumali, J. Math. Phys. 49, 022302 (2008). Crossref, Web of Science, Google Scholar
26. A. Boumali, J. Math. Phys. 54, 099902 (2013). Crossref, Web of Science, Google Scholar