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DKP Equation in the q-deformed Quantum Mechanics

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Abstract

In this paper, the DKP equation has been studied in q-deformed quantum mechanics. After rewriting the DKP equation in the new formalism, the system of coupled equations for the components of the wave function has been decoupled. Then, three problems of one-dimensional scattering have been studied in detail. Effects of the deformation parameter, potential constant, and other parameters have been depicted and discussed.

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References

  1. E.M. Corson, Introduction to Tensors, Spinors and Relativistic Wave Equations (relation structure) (Blackie and Son, London, 1953)

    MATH  Google Scholar 

  2. P. Ghose, D. Home, M.N.S. Roy, Phys. Lett. A 183, 267 (1993)

    ADS  MathSciNet  Google Scholar 

  3. P. Ghose, D. Home, Phys. Lett. A 191, 362 (1994)

    ADS  Google Scholar 

  4. G. Petiau, A.R. Belg, A. Sci. Mém. Collect. 16, 1 (1936)

    Google Scholar 

  5. G. Petiau, Ph.D Thesis, University of Paris, (1936)

  6. G. Petiau, Acad. R. Belg. Cl. Sci. Mém. Collect. 8, 16 (1936)

    Google Scholar 

  7. N. Kemmer, Proc. R. Soc. A 166, 127 (1938)

    ADS  Google Scholar 

  8. R.J. Duffin, Phys. Rev. 54, 1114 (1938)

    ADS  Google Scholar 

  9. N. Kemmer, Proc. R. Soc. A 173, 91 (1939)

    ADS  MathSciNet  Google Scholar 

  10. B.C. Clark, S. Hama, G.R. Kälbermann, R.L. Mercer, L. Ray, Phys. Rev. Lett. 55, 592 (1985)

    ADS  Google Scholar 

  11. G. Kalbermann, Phys. Rev. C 34, 2240 (1986)

    ADS  Google Scholar 

  12. R.E. Kozack, B.C. Clark, S. Hama, V.K. Mishra, G. Kälbermann, R.L. Mercer, L. Ray, Phys. Rev. C 37, 2898 (1988)

    ADS  Google Scholar 

  13. R.E. Kozack, Phys. Rev. C 40, 2181 (1989)

    ADS  Google Scholar 

  14. V.K. Mishra, S. Hama, B.C. Clark, R.E. Kozack, R.L. Mercer, L. Ray, Phys. Rev. C 43, 801 (1991)

    ADS  Google Scholar 

  15. B.C. Clark, R.J. Furnstahl, L.K. Kerr, J. Rusnak, S. Hama, Phys. Lett. B 427, 231 (1998)

    ADS  Google Scholar 

  16. Y. Nedjadi, R.C. Barrett, J. Phys. G 19, 87 (1993)

    ADS  Google Scholar 

  17. R.E. Kozak, B.C. Clark, S. Hama, V.K. Mishra, R.L. Mercer, L. Ray, Phys. Rev. C 40, 2181 (1989)

    ADS  Google Scholar 

  18. H. Hassanabadi, W.S. Chung, S. Zare, H. Sobhani, Eur. Phys. J. C 78, 83 (2018)

    ADS  Google Scholar 

  19. R.C. Barrett, Y. Nedjadi, Nucl. Phys. A 585, 311c (1995)

    ADS  Google Scholar 

  20. S. Ait-Tahar, J.S. l-Khalili, Y. Nedjadi, Nucl. Phys. A 589, 307 (1995)

    ADS  Google Scholar 

  21. S. Sargolzaeipor, H. Hassanabadi, A. Boumali, Int. J. Geom. Methods Mod. Phys. (2017). https://doi.org/10.1142/S0219887817501122

    Article  Google Scholar 

  22. M. Darroodi, H. Hasaanabadi, Quantum Stud.: Math. Found. (2017). https://doi.org/10.1007/s40509-017-0103-4

    Article  Google Scholar 

  23. H. Sobhani, H. Hassanabadi, Phys. Part. Nuclei Lett. 14, 83 (2017)

    ADS  Google Scholar 

  24. S. Valladares, C. Rojas, Int. J. Mod. Phys. A (2023). https://doi.org/10.1142/S0217751X23500203

    Article  Google Scholar 

  25. O. Langueur, M. Merad, A. Rassoul, Int. J. Mod. Phys. A 36, 2150187 (2021)

    ADS  Google Scholar 

  26. E. Alkis, E.E. Kangal, G. Onengut, A.K. Topaksu, Int. J. Mod. Phys. A 36, 2150079 (2021)

    Google Scholar 

  27. L. Sek, M. Falek, M. Moumni, Int. J. Mod. Phys. A 36, 2150113 (2021)

    ADS  Google Scholar 

  28. A. Saidi, M.B. Sedra, Int. J. Mod. Phys. A 35, 2050014 (2020)

    Google Scholar 

  29. M.A. Hun, N. Candemir, Int. J. Mod. Phys. A 34, 1950056 (2019)

    ADS  Google Scholar 

  30. O. Greenberg, Phys. Rev. D 43, 4111 (1991)

    ADS  MathSciNet  Google Scholar 

  31. D. Bonatsos, C. Daskaloyannis, Prog. Part. Nucl. Phys. 43, 537 (1999)

    ADS  Google Scholar 

  32. P.K. Bera, J. Datta, Pram. J. Phys. 67, 1023 (2006)

    Google Scholar 

  33. M. Chaichian, D. Ellinas, P. Kulish, Phys. Rev. Lett. 65, 980 (1990)

    ADS  MathSciNet  Google Scholar 

  34. M. Chaichian, D. Ellinas, P. Kulish, Chem. Phys. Lett. 302 (1999)

  35. M. Arik, D. Coon, J. Math. Phys. 17, 524 (1976)

    ADS  Google Scholar 

  36. A.J. Macfarlane, J. Phys. A 22, 4581 (1989)

    ADS  MathSciNet  Google Scholar 

  37. L. Biedenharn, J. Phys. A 22 L 873 (1989)

  38. A. Lorek, A. Ruffing, J. Wess, Z. Phys. C 74, 369 (1997)

    MathSciNet  Google Scholar 

  39. I.L. Cooper, R.K. Gupta, Phys. Rev. A 52, 941 (1995)

    ADS  MathSciNet  Google Scholar 

  40. A. Lavagno, A.M. Scarfone, P.N. Swamy, Eur. Phys. J. C 47, 253 (2006)

    ADS  Google Scholar 

  41. D. Bonatsos, D. Daskaloyannis, Prgor. Part. Nucl. Phys. 43, 537 (1999)

    ADS  Google Scholar 

  42. A. Lavagno, Phys. Lett. A 301, 13 (2002)

    ADS  MathSciNet  Google Scholar 

  43. A. Lavagno, Phys. A 305, 238 (2002)

    MathSciNet  Google Scholar 

  44. F. Wilczek, fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990)

    MATH  Google Scholar 

  45. A. Strominger, Phys. Rev. Lett. 71, 3397 (1993)

    ADS  MathSciNet  Google Scholar 

  46. A.J. Macfarlane, J. Phys. A, Math. Gen. 22, 4581 (1989)

    ADS  Google Scholar 

  47. L.C. Biedenharn, J. Phys. A 22, L873 (1989)

    ADS  Google Scholar 

  48. S.A. Alavi, S. Rouhani, Phys. Lett. A 320, 327 (2004)

    ADS  MathSciNet  Google Scholar 

  49. M.R. Monteiro, L.M.C.S. Rodrigues, L. Wulck, Phys. Rev. Lett. 76, 1098 (1996)

    ADS  Google Scholar 

  50. R.S. Johal, R.K. Gupta, Int. J. Mod. Phys. E 7, 553 (1998)

    ADS  Google Scholar 

  51. D. Bonatsos, C. Daskaloyannis, P. Kolokotronis, J. Chem. Phys. 106, 605 (1997)

    ADS  Google Scholar 

  52. H. Sobhani, W.S. Chung, H. Hassanabadi, Ind. J. Phys. (2017). https://doi.org/10.1007/s12648-017-1121-0

    Article  Google Scholar 

  53. W.S. Chung, H. Sobhani, H. Hassanabadi, Eur. Phys. J. Plus 132, 398 (2017)

    Google Scholar 

  54. H. Sobhani, W.S. Chung, H. Hassanabadi, Adv. High Energy Phys. 2017, 9530874 (2017)

    Google Scholar 

  55. J.T. Lunardi, J. Math. Phys. 58, 123501 (2017)

    ADS  MathSciNet  Google Scholar 

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Acknowledgements

It is a great pleasure for the authors to thank the referee because of the helpful comments.

Author information

Authors and Affiliations

  1. Faculty of Physics and Nuclear Engineering, Shahrood University of Technology, Shahrood, P. O. Box: 3619995161-316, Iran

    Hadi Sobhani & Hassan Hassanabadi

  2. Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, Jinju, 52828, Korea

    W. S. Chung

Authors
  1. Hadi Sobhani
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  2. Hassan Hassanabadi
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  3. W. S. Chung
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Contributions

The idea was provided by professors HH and WSC. HS did calculations and derivations together by the professors.

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Correspondence to Hadi Sobhani.

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Sobhani, H., Hassanabadi, H. & Chung, W.S. DKP Equation in the q-deformed Quantum Mechanics. Few-Body Syst 64, 18 (2023). https://doi.org/10.1007/s00601-023-01800-5

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