Skip to main content
Log in

Bound and Scattering State Solutions of the Klein–Gordon Equation with Deng–Fan Potential in Higher Dimensions

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

In this study, the Klein–Gordon equation was solved with the Deng–Fan potential using the Nikiforov–Uvarov-functional-analysis in higher dimensions. By employing the improved Pekeris-type approximation scheme, the relativistic and nonrelativistic energy spectra of the Deng–Fan potential were obtained in closed form. In addition, the scattering state phase shift expression of Deng–Fan potential was obtained in higher dimensions. The effects of the vibrational and rotational quantum numbers on the vibrational energies and scattering phase shift of hydrogen chloride (HCl) and lithium hydride (LiH) diatomic molecules were studied numerically and graphically at different dimensions. Interestingly, there exists inter-dimensional degeneracy symmetry for the scattering phase shift of the diatomic molecular systems considered. Our results generally were in agreement with that obtained from literatures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. M.C. Zhang, B. An, Chin. Phys. Lett. 27, 110301 (2010)

    Article  ADS  Google Scholar 

  2. Y. Sun, S. He, C.S. Jia, Phys. Scr. 87, 025301 (2013)

    Article  ADS  Google Scholar 

  3. C.A. Onate, Afr. Rev. Phys. 8, 325 (2013)

    Google Scholar 

  4. C.A. Onate, M.C. Onyeaju, A.N. Ikot, Ann. Phys. 375, 239 (2016)

    Article  ADS  Google Scholar 

  5. C.A. Onate, O. Adebimpe, A.F. Lukman, I.J. Ibrahim, J.O. Okoro, E.O. Davids, Heliyon 4, e00977 (2018)

    Article  Google Scholar 

  6. U.S. Okorie, E.E. Ibekwe, M.C. Onyeaju, A.N. Ikot, Eur. Phys. J. Plus 133, 433 (2018)

    Article  Google Scholar 

  7. A.N. Akpan, E.O. Chukwuocha, M.C. Onyeaju, C.A. Onate, B.I. Ita, M.E. Udoh, Pramana. J. Phys. 90, 22 (2018)

    Google Scholar 

  8. M. Abu-Shady, Int. J. Appl. Math. Theor. Phys. 16, 2 (2015)

    Google Scholar 

  9. C.O. Edet, U.S. Okorie, A.T. Ngiangia, A.N. Ikot, Ind. J. Phys. 94(4), 425 (2020)

    Article  Google Scholar 

  10. E.E. Ibekwe, A.T. Ngiangia, U.S. Okorie, A.N. Ikot, H.Y. Abdullah, Iran J. Sci. Tech. Trans. Sci. (2020). https://doi.org/10.1007/s40995-020-00913-4

  11. A.N. Ikot, C.O. Edet, P.O. Amadi, U.S. Okorie, G.J. Rampho, H.Y. Abdullah, Eur. Phys. J. D 74, 159 (2020)

    Article  ADS  Google Scholar 

  12. J.B. Tang, Y.T. Wang, X.L. Peng, L.H. Zhang, C.S. Jia, J. Mol. Struct. 1199, 126958 (2020)

    Article  Google Scholar 

  13. H. Ciftci, R.L. Hall, N. Saad, J. Phys. A: Math. Gen. 36, 11807 (2003)

    Article  ADS  Google Scholar 

  14. A. F. Nikiforov, V. B. Uvarov, Special Functions of Mathematical Physics ed A Jaffe (Germany: BirkhauserVerlag Basel) p 317 (1988)

  15. E. Witten, Nucl. Phys. B 188, 513 (1981)

    Article  ADS  Google Scholar 

  16. M.R. Setare, E. Karimi, Phys. Scr. 75, 90 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  17. Z.O. Ma, B.W. Xu, Euro. Phys. Lett. 69, 685 (2005)

    Article  ADS  Google Scholar 

  18. J.Y. Liu, G.D. Zhang, C.S. Jia, Phys. Lett. A 377, 1444 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  19. M. Abusini, M. Serhan, M.F. Al-Jamal, A. Al-Jamel, E.M. Rabel, Pramana J. Phys. 93, 93 (2019)

  20. G. Chen, Phys. Lett. A 326, 55 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  21. S.H. Dong, Factorization Method in Quantum Mechanics (Springer, Amsterdam, 2007)

    Book  MATH  Google Scholar 

  22. H.M. Tang, G.C. Liang, L.H. Zhang, F. Zhao, C.S. Jia, Can. J. Chem. 92, 341 (2014)

    Article  Google Scholar 

  23. C.S. Jia, Y. Jia, Eur. Phys. J. D 71, 3 (2017)

    Article  ADS  Google Scholar 

  24. A.N. Ikot, G.J. Rampho, P.O. Amadi, M.J. Sithole, U.S. Okorie, M.I. Lekala, Eur. Phys. J. Plus 135, 503 (2020)

    Article  Google Scholar 

  25. G. J. Rampho, A. N. Ikot, C. O. Edet, U. S. Okorie, Mol. Phys. e1821922 (2020). https://doi.org/10.1080/00268976.2020.1821922

  26. A. N. Ikot, G. J. Rampho, P. O. Amadi, U. S. Okorie, M. J. Sithole, M. L. Lekala, Int. J. Quant. Chem. e26410 (2020). https://doi.org/10.1002/qua.26410

  27. A.N. Ikot, U.S. Okorie, G.J. Rampho, P.O. Amadi, Int. J. Thermophys. 42, 10 (2021)

    Article  ADS  Google Scholar 

  28. O. Klein, Z. Phys. 37, 895 (1926)

    Article  ADS  Google Scholar 

  29. S. Flugge, Practical Quantum Mechanics (Springer, Berlin, 1994)

    MATH  Google Scholar 

  30. W. Greiner, Relativistic Quantum Mechanics: Wave Equations, 3rd edn. (Springer, Berlin, 2000)

    Book  MATH  Google Scholar 

  31. S.H. Dong, Wave Equations in Higher Dimensions (Springer, New York, 2011)

    Book  MATH  Google Scholar 

  32. X.J. Xie, C.S. Jia, Phys. Scr. 90, 035207 (2015)

    Article  ADS  Google Scholar 

  33. S.H. Dong, S.H. Dong, H. Bahl Ouli, V.B. Bezerra, Int. J. Mod. Phys. E 20, 55 (2011)

    Article  ADS  Google Scholar 

  34. C.N. Isonguyo, I.B. Ituen, A.N. Ikot, H. Hassanabadi, Bull. Kor. Chem. Soc. 35, 3443 (2014)

    Article  Google Scholar 

  35. A.N. Ikot, B.I. Ita, O.A. Awoga, Few-Body Syst. 53, 539 (2012)

    Article  ADS  Google Scholar 

  36. A.D. Antia, A.N. Ikot, H. Hassanabadi, E. Maghsoodi, Ind. J. Phys. 87, 1133 (2013)

    Article  Google Scholar 

  37. A.N. Ikot, H. Hassanabadi, H.P. Obong, Y.E. Chad-Umoren, C.N. Isonguyo, B.H. Yazarloo, Chin. Phys. B 23, 120303 (2014)

    Article  Google Scholar 

  38. A.N. Ikot, O.A. Awoga, A.D. Antia, H. Hassanabadi, E. Maghsoodi, Few-Body Syst. 54, 2014 (2013)

    Google Scholar 

  39. U.S. Okorie, A.N. Ikot, C.O. Edet, I.O. Akpan, R. Sever, G.J. Rampho, J. Phys. Commun. 3, 095015 (2019)

    Article  Google Scholar 

  40. C.Y. Chen, F.L. Lu, D.S. Sun, Commun. Theor. Phys. 45, 889 (2006)

    Article  ADS  Google Scholar 

  41. C.Y. Chen, L.F. Lu, Y. You, Chin. Phys. B 21, 030302 (2012)

    Article  ADS  Google Scholar 

  42. W.G. Feng, C.W. Li, W.H. Ying, L.Y. Yuan, Chin. , Phys. B 18, 3663 (2009)

  43. C.Y. Chen, D.S. Sun, F.L. Lu, Phys. Lett. A 330, 424 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  44. H. Hassanabadi, B.H. Yazarloo, Ind. J. Phys. 87, 1017 (2013)

    Article  Google Scholar 

  45. A. Tas, A. Havare, Few-Body Syst. 59, 52 (2018)

    Article  Google Scholar 

  46. A.N. Ikot, H.P. Obong, T.M. Abbey, S. Zare, M. Ghanfourian, H. Hassanabadi, Few- Body Syst. 57, 807 (2016)

    Article  ADS  Google Scholar 

  47. U.S. Okorie, A.N. Ikot, C.O. Edet, G.J. Rampho, R. Horchani, H. Jelassi, Eur. Phys. J. D 75, 53 (2021)

    Article  ADS  Google Scholar 

  48. Z.H. Deng, Y.P. Fan, Shandong Univ. J. 7, 162 (1957)

    Google Scholar 

  49. K.J. Oyewumi, O.J. Oluwadare, K.D. Sen, O.A. Babalola, J. Math. Chem. 51, 976 (2013)

    Article  MathSciNet  Google Scholar 

  50. H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, H. Rahimov, Commun. Theor. Phys. 57, 339 (2012)

    Article  ADS  Google Scholar 

  51. H. Hassanabadi, S. Zarrinkamar, H. Rahimov, Commun. Theor. Phys. 56, 423 (2011)

    Article  ADS  Google Scholar 

  52. L.H. Zhang, X.P. Li, C.S. Jia, Int. J. Quant. Chem. 111, 1870 (2011)

    Article  Google Scholar 

  53. A.N. Ikot, G.J. Rampho, P.O. Amadi, M.J. Sithole, U.S. Okorie, M.I. Lekala, Eur. Phys. J. Plus 135, 503 (2020)

    Article  Google Scholar 

  54. A.N. Ikot, U.S. Okorie, G.J. Rampho, P.O. Amadi, C.O. Edet, I.O. Akpan, H.Y. Abdullah, R. Horchani, J. Low Temp. Phys. (2021). https://doi.org/10.1007/s10909-020-02544-w

  55. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965)

    MATH  Google Scholar 

  56. C.Y. Chen, D.S. Sun, C.L. Liu, F.L. Lu, Commun. Theor. Phys. 55, 399 (2011)

    Article  ADS  Google Scholar 

  57. M. Lacombe, B. Loiseau, J.M. Richard et al., Phys. Rev. C 21, 861 (1980)

    Article  ADS  Google Scholar 

  58. W. Schwinger, W. Plessas, L.P. Kok, H. van Haeringen, Phys. Rev. C 27, 515 (1983)

    Article  ADS  Google Scholar 

  59. J. Haidenbauer, W. Plessas, Phys. Rev. C 30, 1822 (1984)

    Article  ADS  Google Scholar 

  60. J. Bhoi, U. Laha, Phys. Atm. Nucl. 78, 831 (2015)

    Article  ADS  Google Scholar 

  61. O.J. Oluwadare, K.J. Oyewumi, Eur. Phys. J. A 53, 29 (2017)

    Article  ADS  Google Scholar 

  62. D.R. Herschbach, J. Avery, O. Goscinski, Dimensional Scaling in Chemical Physics (Kluwer Academic Publishers, Springer Science, Berlin, 1993)

    Book  Google Scholar 

  63. A. Svidzinsky, G. Chen, S. Chin, M. Kim, D. Ma, R. Murawski, A. Sergeev, M. Scully, D. Herschbach, Int. Rev. Phys. Chem. 27, 665 (2008)

    Article  Google Scholar 

  64. C.J. Jia, J.W. Dai, L.H. Zhang, J.Y. Liu, G.D. Zhang, Chem. Phys. Lett. 619, 54 (2015)

    Article  ADS  Google Scholar 

  65. Z. Ding, G. Chen, C.S. Lin, J. Math. Phys. 51, 123508 (2010)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors NAA acknowledged the financial support from Taif University Researchers Supporting Project number (TURSP-2020/247), Taif University, Taif, Saudi Arabia.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. N. Ikot or U. S. Okorie.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ikot, A.N., Okorie, U.S., Rampho, G.J. et al. Bound and Scattering State Solutions of the Klein–Gordon Equation with Deng–Fan Potential in Higher Dimensions. Few-Body Syst 62, 101 (2021). https://doi.org/10.1007/s00601-021-01693-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-021-01693-2

Navigation