Skip to main content
SpringerLink
Log in

Dirac Equation with Coupling to 1/r Singular Vector Potentials for all Angular Momenta

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials.

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. Flügge, S.: Practical Quantum Mechanics. Springer, New York (1974)

    Google Scholar 

  2. Pekeris, C.L.: Phys. Rev. 45, 98 (1934)

    Article  MATH  ADS  Google Scholar 

  3. Arda, A., Sever, R.: Int. J. Theor. Phys. 48, 945 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Xu, Y., He, S., Jia, C.-S.: J. Phys. A 41, 255302 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  5. Zhang, Y.: Phys. Scr. 78, 015006 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  6. Qiang, W.-C., Dong, S.-H.: Phys. Lett. A 372, 4789 (2008)

    Article  ADS  Google Scholar 

  7. Zhang, L.-H., Li, X.-P., Jia, C.-S.: Phys. Lett. A 372, 2201 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  8. Chen, C.-Y., Lu, F.-L., Sun, D.-S.: Cent. Eur. J. Phys. 6, 884 (2008)

    Google Scholar 

  9. Chen, C.-Y., Sun, D.-S., Lu, F.-L.: Phys. Lett. A 370, 219 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  10. Chen, G.: Mod. Phys. Lett. A 19, 2009 (2004)

    Article  MATH  ADS  Google Scholar 

  11. Chen, G., Chen, Z.-D., Lou, Z.-M.: Phys. Lett. A 331, 374 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. Roy, B., Roychoudhury, R.: J. Phys. A 29, 2919 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  13. Roy, B., Roychoudhury, R.: J. Phys. A 23, 5095 (1990)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Dominguez-Adame, F.: Phys. Lett. A 136, 175 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  15. Hulthén, L.: Ark. Mat. Astron. Fys. A 28, 5 (1942)

    Google Scholar 

  16. Hulthén, L.: Ark. Mat. Astron. Fys. B 29, 1 (1942)

    Google Scholar 

  17. Hulthén, L., Sugawara, M.: In: Flügge, S. (ed.) Encyclopedia of Physics, vol. 39. Springer, Berlin (1957)

    Google Scholar 

  18. Eckart, C.: Phys. Rev. 35, 1303 (1930)

    Article  ADS  Google Scholar 

  19. Greiner, W.: Relativistic Quantum Mechanics: Wave Equations. Springer, Berlin (1994)

    Google Scholar 

  20. Bjorken, J.D., Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1964)

    Google Scholar 

  21. Witten, E.: Nucl. Phys. B 185, 513 (1981)

    Article  ADS  Google Scholar 

  22. Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995)

    Article  MathSciNet  Google Scholar 

  23. Alhaidari, A.D.: J. Phys. A 37, 5805 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Sinha, A., Roychoudhury, R., Varshni, Y.P.: Can. J. Phys. 78, 141 (2000)

    Article  ADS  Google Scholar 

  25. Stubbins, C.: Phys. Rev. A 48, 220 (1993)

    Article  ADS  Google Scholar 

  26. Varshni, Y.P.: Phys. Rev. A 41, 4682 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  27. Matthys, P., De Meyer, H.: Phys. Rev. A 38, 1168 (1988)

    Article  ADS  Google Scholar 

  28. Tang, A.Z., Chan, F.T.: Phys. Rev. A 35, 911 (1987)

    Article  ADS  Google Scholar 

  29. Dutt, R., Mukherji, U.: Phys. Lett. A 98, 395 (1982)

    Article  ADS  Google Scholar 

  30. Greene, R.L., Aldrich, C.: Phys. Rev. A 14, 2363 (1976)

    Article  ADS  Google Scholar 

  31. Qian, S.-W., Huang, B.-W., Gu, Z.-Y.: New J. Phys. 4, 13.1 (2002)

    Article  Google Scholar 

  32. Jia, C.-S., Liu, J.-Y., Wang, P.-Q.: Phys. Lett. A 372, 4779 (2008)

    Article  ADS  Google Scholar 

  33. Ikhdair, S.M., Sever, R.: J. Math. Chem. 42, 461 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  34. Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer, New York (1966)

    MATH  Google Scholar 

  35. Diao, Y.-F., Yi, L.-Z., Chen, T., Jia, C.-S.: Mod. Phys. Lett. B 23, 2269 (2009)

    Article  MATH  ADS  Google Scholar 

  36. Wei, G.-F., Long, C.-Y., Duan, X.-Y., Dong, S.-H.: Phys. Scr. 77, 035001 (2008)

    Article  ADS  Google Scholar 

  37. Dong, S.-H., Qiang, W.-C., Sun, G.-H., Bezerra, V.B.: J. Phys. A 40, 10535 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Author information

Author notes

  1. A. D. Alhaidari

    Present address: , 1300 Midvale Ave. #307, Los Angeles, CA, 90024, USA

Authors and Affiliations

  1. Saudi Center for Theoretical Physics, Dhahran, Saudi Arabia

    A. D. Alhaidari

  2. Physics Department, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

    A. D. Alhaidari

Authors
  1. A. D. Alhaidari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. D. Alhaidari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alhaidari, A.D. Dirac Equation with Coupling to 1/r Singular Vector Potentials for all Angular Momenta. Found Phys 40, 1088–1095 (2010). https://doi.org/10.1007/s10701-010-9431-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-010-9431-5

Keywords

Search

Navigation