Research PaperNo Access

Laboratoire LRPPS, Université de Kasdi Merbah-Ouargla, BP 511, Route Ghardaia, 30000 Ouargla, Algérie

E-mail Address: benzair.hadjira@gmail.com

Corresponding author.

Search for more papers by this author

T. Boudjedaa

Laboratoire de Physique Théorique, Université de Jijel BP98 Ouled Aissa, 18000 Jijel, Algérie

Search for more papers by this author

, and

M. Merad

Laboratoire (L.S.D.C), Université de Oum El Bouaghi, 04000 Oum El Bouaghi, Algérie

Search for more papers by this author

https://doi.org/10.1142/S0217751X2450146XCited by:0 (Source: Crossref)

Abstract

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined.

Keywords:

PACS: 03.65.Pm, 03.65.Ca, 03.65.Db, 03.65.Ge

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. C. F. Dunkl , Math. Z. 197, 33 (1988). Crossref, Web of Science, Google Scholar
2. C. F. Dunkl , Trans. Am. Math. Soc. 311, 167 (1989). Crossref, Web of Science, Google Scholar
3. E. P. Wigner , Phys. Rev. 77, 711 (1950). Crossref, Web of Science, ADS, Google Scholar
4. L. M. Yang , Phys. Rev. 84, 788 (1951). Crossref, Web of Science, ADS, Google Scholar
5. W. S. Chung and H. Hassanabadi , Modern Phys. Lett. A 34, 1950190 (2019). Link, Web of Science, ADS, Google Scholar
6. H. Hassanabadi, M. de Montigny, W. S. Chung and P. Sedaghatnia , Physica A 580, 126154 (2021). Crossref, Web of Science, Google Scholar
7. S. Hassanabadi, P. Sedaghatnia, W. S. Chung, B. C. Lütfüoğlu, J. Kriz and H. Hassanabadi , Eur. Phys. J. Plus 138, 1 (2023). Crossref, Web of Science, Google Scholar
8. R. D. Mota and D. Ojeda-Guillén , Modern Phys. Lett. A 37, 2250006 (2022). Link, Web of Science, ADS, Google Scholar
9. A. Ballesteros, A. Najafizade, H. Panahi, H. Hassanabadi and S. H. Dong , Ann. Phys. 460, 169543 (2024). Crossref, Web of Science, Google Scholar
10. H. Bouguerne, B. Hamil, B. C. Lütfüoğlu and M. Merad , Indian J. Phys. 98, 4093 (2024). Crossref, Google Scholar
11. C. Quesne , J. Phys. A: Math. Theor. 56, 265203 (2023). Crossref, Web of Science, ADS, Google Scholar
12. A. Merad and M. Merad , Few-Body Syst. 62, 1 (2021). Crossref, Web of Science, Google Scholar
13. B. Hamil and B. C. Lütfüoğlu , Eur. Phys. J. Plus 137, 1 (2022). Web of Science, Google Scholar
14. B. Hamil and B. C. Lütfüoğlu , Few-Body Syst. 63, 74 (2022). Crossref, Web of Science, ADS, Google Scholar
15. W. S. Chung and H. Hassanabadi , Eur. Phys. J. Plus 136, 1 (2021). Crossref, Web of Science, Google Scholar
16. N. Rouabhia, M. Merad and B. Hamil , Europhys. Lett. 143, 52003 (2023). Crossref, ADS, Google Scholar
17. P. Sedaghatnia, H. Hassanabadi, G. Junker, J. Kriz, S. Hassanabadi and W. S. Chung , Ann. Phys. 458, 169445 (2023). Crossref, Web of Science, Google Scholar
18. S. H. Dong, W. H. Huang, W. S. Chung, P. Sedaghatnia and H. Hassanabadi , Europhys. Lett. 135, 30006 (2021). Crossref, ADS, Google Scholar
19. R. D. Mota and D. Ojeda-Guillén , Modern Phys. Lett. A 37, 2250224 (2022). Link, Web of Science, ADS, Google Scholar
20. S. Hassanabadi, J. Kříž, B. C. Lütfüoğlu and H. Hassanabadi , Phys. Scr. 97, 125305 (2022). Crossref, Web of Science, ADS, Google Scholar
21. G. Junker , J. Phys. A: Math. Theor. 57, 075201 (2024). Crossref, Web of Science, Google Scholar
22. H. Benzair, T. Boudjedaa and M. Merad , Phys. Scr. 99, 055261 (2024). Crossref, Web of Science, Google Scholar
23. M. Rosenblum , Oper. Theory Adv. Appl. 73, 369 (1994). Google Scholar
24. W. S. Chung, G. Junker, S. H. Dong and H. Hassanabadi , Europhys. Lett. 141, 32001 (2023). Crossref, ADS, Google Scholar
25. D. C. Khandekar, S. V. Lawande and K. V. Bhagwat , Path Integral Methods and Their Applications (1986). Google Scholar
26. I. S. Gradshteyn and I. M. Ryzhik , Table of Integrals, Series, and Products, Corrected and Enlarged Edition ( Academic Press Inc., New York, 1980). Google Scholar
27. C. Grosche and F. Steiner , Handbook of Feynman Path Integrals, Springer Tracts in Modern Physics, Vol. 145 ( Springer, Berlin, Heidelberg, 1998). Crossref, Google Scholar