Skip to main content
SpringerLink
Log in

Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

In this paper, we study the approximate analytical solutions for bound states of the l-wave Klein-Gordon equation with a position-dependent mass subjected to a hyperbolic cotangent vector potential by using the concept of the supersymmetric quantum mechanics approach. Within the framework of the proper approximation of the centrifugal term, we obtain the bound state energy eigenvalues and the corresponding normalized wavefunctions written down in terms of the Jacobi polynomials. Furthermore, it is found that the solutions in the case of constant mass for nonzero l-values are identical to the ones obtained in the literature. Among these cases, Hulthén potential, Coulomb potential, and nonrelativistic limit are discussed

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L Chetouani, L Guechi, A Lecheheb and T F Hammann Physica A 234 529 (1996)

    ADS  Google Scholar 

  2. F Benamira, L Guechi, S Mameri and M A Sadoun J. Math. Phys. 51 032301 (2010)

    ADS  MathSciNet  Google Scholar 

  3. A Khodja, A Kadja, F Benamira and L Guechi Indian J Phys 91 1561 (2017)

    ADS  Google Scholar 

  4. A Kadja, F Benamira and L Guechi Indian J Phys 91 259 (2016)

    ADS  Google Scholar 

  5. B J Falaye Cent. Eur. J. Phys. 10 960 (2012)

    Google Scholar 

  6. N Saad, R L Hall and H Ciftci Cent. Eur. J. Phys. 6 717 (2008)

    Google Scholar 

  7. A Antia, A Ikot, H Hassanabadi and E Maghsoodi Indian. J. Phys. 87 11 (2013)

    Google Scholar 

  8. P Aspoukeh and S M Hamad Chin. J. Phys. 68 224 (2020)

    Google Scholar 

  9. A Ahmadov, M Demirci, S Aslanova and M Mustamin Phys. Lett. A. 384 126372 (2020)

    MathSciNet  Google Scholar 

  10. R H Parmar and P C Vinodkumar J. Math. Chem. 59 1638 (2021)

    MathSciNet  Google Scholar 

  11. Y Xu, S He and C S Jia Phys. Scr. 81 045001 (2010)

    ADS  Google Scholar 

  12. C S Jia, T Chen and S He Phys. Lett. A 377 9 (2013)

    Google Scholar 

  13. F Tajik, Z Sharifi, M Eshghi, M Hamzavi, M Bigdeli and S M Ikhdair Physica A 535 122497 (2019)

    MathSciNet  Google Scholar 

  14. A Arda and R Sever Mod. Phys. Lett. A 27 1250171 (2012)

    ADS  Google Scholar 

  15. F Dominguez-adame Phys. Lett. A 136 175 (1989)

    ADS  MathSciNet  Google Scholar 

  16. S Haouat and L Chetouani Phys. Scr. 77 025005 (2008)

    ADS  Google Scholar 

  17. F Benamira, L Guechi and A Zouache Phys. Lett. A 372 7199 (2008)

    ADS  MathSciNet  Google Scholar 

  18. F Benamira, L Guechi and A Zouache Phys. Lett. A 367 498 (2007)

    ADS  MathSciNet  Google Scholar 

  19. W C Qiang and S H Dong Phys. Lett. A 372 4789 (2008)

    ADS  Google Scholar 

  20. O Von Roos Phys. Rev. B 27 7547 (1983)

    ADS  Google Scholar 

  21. F Arias de Saavedra, J Boronat, A Polls and A Fabrocini Phys. Rev. B 50 4248 (1994)

  22. L Serra and E Lipparini Eur. Phys. Lett. 40 667 (1997)

    ADS  Google Scholar 

  23. M Barranco, M Pi, S M Gatica, E S Hernndez and J Navarro Phys. Rev. B 56 8997 (1997)

    ADS  Google Scholar 

  24. A Puente, L Serra and M Z Casas Phys. D 31 283 (1994)

    ADS  Google Scholar 

  25. M R Geller and W Kohn Phys. Rev. Lett. 70 3103 (1993)

    ADS  Google Scholar 

  26. F Serafim, F A N Santos, J R F Lima, C Filgueiras and F Moraes Physica. E 108 139 (2019)

    ADS  Google Scholar 

  27. Dutra A de Souza and C A S Almeida Phys. Lett. A 275 25 (2000)

    ADS  MathSciNet  Google Scholar 

  28. B Bagchi, P Gorain, C Quesne and R Roychoudhury Europhys. Lett. 72 155 (2005)

    ADS  MathSciNet  Google Scholar 

  29. H Rajbongshi Indian. J. Phys. 92 357 (2018)

    ADS  Google Scholar 

  30. Q Yu, K Guo, M Hu, Z Zhang and D Liu J. Opt. Soc. Am. B 35 1408 (2018)

    ADS  Google Scholar 

  31. C S Jia, X P Li and L H Zhang Few-Body Syst. 52 11 (2012)

    ADS  Google Scholar 

  32. T Q Dai and Y F Cheng Phys. Scr. 79 015007 (2009)

    ADS  Google Scholar 

  33. A Arda, R Sever and C Tezcan Phys. Scr. 79 015006 (2009)

    ADS  Google Scholar 

  34. A Arda and R Sever Int. J. Theor. Phys. 48 945 (2009)

    Google Scholar 

  35. N Zaghou, F Benamira and L Guechi Indian. J. Phys. 96 1105 (2022)

    ADS  Google Scholar 

  36. S M Ikhdair and B J Falaye Eur. Phys. J. Plus 129 1 (2014)

    Google Scholar 

  37. S Medjenah and F Benamira Indian. J. Phys. 97 141 (2023)

    ADS  Google Scholar 

  38. S Bouledjedj, A Khodja, F Benamira and L Guechi Can. J. Phys. 100 493 (2022)

    ADS  Google Scholar 

  39. H Egrifes and R Sever Int. J. Theor. Phys. 46 935 (2007)

    Google Scholar 

  40. N Zaghou, F Benamira and L Guechi Eur. Phys. J. Plus 132 40 (2017)

    Google Scholar 

  41. A Sinha and P Roy Mod. Phys. Lett. A 20 2377 (2005)

    ADS  Google Scholar 

  42. C S Jia and A de Souza Dutra Ann. Phys. 323 566 (2008)

  43. O Mustafa and S H Mazharimousavi Int. J. Theor. Phys. 47 1112 (2008)

    Google Scholar 

  44. L B Castro Phys. Lett. A 375 2510 (2011)

    ADS  MathSciNet  Google Scholar 

  45. R L Greene and C Aldrich Phys. Rev. A 14 6 (1976)

    Google Scholar 

  46. F Cooper, A Khare and U P Sukhateme Phys. Rep. 251 267 (1995)

    ADS  MathSciNet  Google Scholar 

  47. N Zaghou, F Benamira and L Guechi Indian. J. Phys. 95 1445 (2021)

    ADS  Google Scholar 

  48. L E Gendenshtein JETP Lett. 38 356 (1983)

    ADS  Google Scholar 

  49. R Dutt, A Khare and U P Sukhatme Phys. Let. B 181 295 (1986)

    ADS  Google Scholar 

  50. J W Dabrowska, A Khare and U P Sukhatme J. Phys. A: Math. Gen. 21 L195 (1988)

    ADS  Google Scholar 

  51. I S Gradshteyn and I M Ryzhik Tables of Integrals, Series and Products (New York: Academic Press) (2007)

    Google Scholar 

  52. L Hulthén Ark. Mat. Astron. Fys. A 28 5 (1942)

    MathSciNet  Google Scholar 

  53. S M Ikhdair and R Sever J. Math. Chem. 42 461 (2007)

    MathSciNet  Google Scholar 

  54. H I Ahmadov, S I Jafarzade and M V Qocayeva Int. J. of Mod. Phys. A 30 1550193 (2015)

    ADS  Google Scholar 

  55. J B Seaborn Hypergeometric Functions and Their Applications (New York: Springer-Verlag) (1991)

    Google Scholar 

  56. W Greiner Relativistic Quantum Mechanics (Berlin: Springer) (2000)

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the Algerian government for the financial assistance allocated within the framework of PRFU project under the code B00L02UN250120220019.

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Frères Mentouri Constantine 1, Route d’Ain El-Bey, 25000, Constantine, Algeria

    N. Zaghou & F. Benamira

  2. Ecole Normale Supérieure Assia Djebar de Constantine, Ville Universitaire Ali Mendjeli, 25000, Constantine, Algeria

    N. Zaghou

Authors
  1. N. Zaghou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Benamira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Zaghou.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zaghou, N., Benamira, F. Supersymmetric approach to approximate analytical solutions of the Klein-Gordon equation: application to a position-dependent mass and a hyperbolic cotangent vector potential. Indian J Phys 98, 2093–2103 (2024). https://doi.org/10.1007/s12648-023-02976-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-023-02976-6

Keywords

Search

Navigation