Skip to main content
SpringerLink
Log in

Downward relativistic potential step and phenomenological account of Bohmian trajectories of the Klein paradox

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

The Dirac equation has been applied to fermions scattering from the downward potential step. The results show that some particles do not fall off the edge of the step and reflect. Then, based on the de Broglie-Bohm interpretation of quantum mechanics (Bohmian mechanics) and Bohmian trajectories we have resolved the problem. Lastly, a phenomenological study of the Bohmian trajectory of the Klein paradox has been 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. O. Klein, Z. Phys. 53, 157 (1929)

    Article  ADS  Google Scholar 

  2. A. Calogeracos, N. Dombey, Contemp. Phys. 40, 313 (1999)

    Article  ADS  Google Scholar 

  3. L.D. Landau, E.M. Lifshitz, Quantum Mechanics, 3rd edition (Oxford, Pergamon, 1977), p. 182

  4. J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics (Mc Graw-Hill, New York, 1964)

  5. S. De Leo, P. Rotelli, Phys. Rev. A 73, 042107 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  6. W. Greiner, Relativistic Quantum Mechanics: wave equations, 3rd ed. (Springer, Berlin, 2000)

  7. P.R. Holland, Found. Phys. 22, 10 (1992)

    Article  Google Scholar 

  8. G. Grübl, R. Moser, K. Rheinberger, J. Phys. A: Math. Gen. 34, 2753 (2001)

    Article  ADS  Google Scholar 

  9. P.R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993)

  10. A. Kyprianidis, Phys. Lett. A 111, 111 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  11. I. Licata, D. Fiscaletti, Quantum Potential: Physics, Geometry and Algebra (Springer, Berlin, 2014)

  12. D. Dürr, S. Goldstein, N. Zanghi, J. Stat. Phys. 67, 843 (1992)

    Article  ADS  Google Scholar 

  13. M. Atiq, M. Karamian, M. Golshani, Ann. Fond. Louis de Broglie 34, 67 (2009)

    MathSciNet  Google Scholar 

  14. M. Mollai, M. Razavi, S. Jami, A. Ahanj, Eur. Phys. J. Plus 128, 1 (2013)

    Article  Google Scholar 

  15. D. Bohm, Prog. Theor. Phys. 9, 273 (1953)

    Article  ADS  Google Scholar 

  16. T. Takabayasi, Suppl. Prog. Theor. Phys. 4, 1 (1957)

    Article  ADS  Google Scholar 

  17. P.L. Garrido, Sh. Goldstein, J. Lakkarinen, R. Tumulka, Am. J. Phys. 79, 1218 (2011)

    Article  ADS  Google Scholar 

  18. F. Sauter, Z. Phys. 69, 742 (1931)

    Article  ADS  Google Scholar 

  19. T. Takabayashi, Prog. Theor. Phys. 9, 187 (1953)

    Article  ADS  Google Scholar 

  20. J.O. Hirschfelder, A.C. Christoph, W.E. Palke, J. Chem. Phys. 61, 5435 (1974)

    Article  ADS  Google Scholar 

  21. T.P. Spiller, T.D. Clark, R.J. Prance, H. Prance, Europhys. Lett. 12, 1 (1990)

    Article  ADS  Google Scholar 

  22. C. Dewdney, B.J. Hiley, Found. Phys. 12, 27 (1982)

    Article  ADS  Google Scholar 

  23. T. Norsen, Am. J. Phys. 81, 258 (2013)

    Article  ADS  Google Scholar 

  24. D. Dragoman, Phys. Scr. 79, 015003 (2009)

    Article  ADS  Google Scholar 

  25. J.R. Williams, L. DiCarlo, C.M. Marcus, Science 317, 638 (2007)

    Article  ADS  Google Scholar 

  26. T.G. Phillips, Nature 529, 294 (2016)

    Article  ADS  Google Scholar 

  27. G. Chardin, Hyperfine Interact. 109, 83 (1997)

    Article  ADS  Google Scholar 

  28. G. Chardin, J.-M. Rax, Phys. Lett. B 282, 256 (1992)

    Article  ADS  Google Scholar 

  29. A. Ramani, J.L. Puget, Astron. Astrophys. 51, 411 (1976)

    ADS  Google Scholar 

  30. A. Benoit-Lévy, G. Chardin, Astron. Astrophys. 537, A78 (2012)

    Article  ADS  Google Scholar 

  31. M.M. Nieto, T. Goldman, Phys. Rep. 205, 221 (1991)

    Article  ADS  Google Scholar 

  32. K.N. Prasanna Kumar, B.S. Kiranagi, C.S. Bagewadi, Adv. Nat. Sci. 5, 14 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Islamic Azad University, Mashhad Branch, 91735-413, Mashhad, Iran

    M. Razavi, M. Mollai & S. Jami

  2. Department of Physics, Khayyam Higher Education Institute (KHEI), Mashhad, Iran

    A. Ahanj

  3. School of Physics, Institute for Research in Fundamental Science (IPM), Tehran, Iran

    A. Ahanj

Authors
  1. M. Razavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Mollai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Jami
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Ahanj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Razavi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Razavi, M., Mollai, M., Jami, S. et al. Downward relativistic potential step and phenomenological account of Bohmian trajectories of the Klein paradox. Eur. Phys. J. Plus 131, 306 (2016). https://doi.org/10.1140/epjp/i2016-16306-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2016-16306-1

Search

Navigation