Skip to main content
SpringerLink
Log in

Low momentum scattering of the Dirac particlewith an asymmetric cusp potential

  • Theoretical Physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

Abstract.

We study the exact solutions of the bound and scattering states of the one-dimensional Dirac equation with an asymmetric cusp potential and derive the condition of the supercriticality for this quantum system. We find that the scattering properties are invariant under reflection of the potential's shape, and the supercritical value for the potential amplitude V 0 varies with the degree of the potential asymmetry.

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.I. Schiff, Quantum mechanics, 3rd ed. (McGraw-Hill, New York 1955)

  2. R.G. Newton, Scattering theory of waves and particles (Springer, Berlin 1982)

  3. D. Bohm, Quantum mechanics (Prentice-Hall, New York 1951)

  4. M. Sassoli de Bianchi, J. Math. Phys 35, 2719 (1994); A. Edgar, Am. J. Phys. 63, 136 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Y.S. Joe, D.S. Ikeler, R.M. Cosby, A.M. Satanin, C.S. Kim, J. Appl. Phys. 88, 2704 (2000)

    Article  ADS  Google Scholar 

  6. B.L. Coulter, C.G. Adler, Am. J. Phys. 39, 305 (1971)

    Article  Google Scholar 

  7. N. Dombey, P. Kennedy, A. Calogeracos, Phys. Rev. Lett. 85, 1787 (2000); A. Calogeracos, N. Dombey, K. Imagawa, Phys. Ato. Nucl. 159, 1275 (1996)

    Article  ADS  Google Scholar 

  8. H.G. Dosch, J.H.D. Jensen, V.F. Müller, Phys. Norvegica 5, 151 (1971)

    Google Scholar 

  9. P. Kennedy, J. Phys. A: Math. Gen. 35, 689 (2002)

    Article  ADS  MATH  Google Scholar 

  10. V.M. Villalba, W. Greiner, Phys. Rev. A 67, 052707 (2003)

    Article  ADS  Google Scholar 

  11. P. Kennedy, N. Dombey, J. Phys. A: Math. Gen 35, 6645 (2002)

    Article  ADS  MATH  Google Scholar 

  12. Z.Q. Ma, G.J. Ni, Phys. Rev. D 31, 1482 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  13. S.H. Dong, X.W. Hou, Z.Q. Ma, Phys. Rev. A 58, 2790 (1998); S.H. Dong, X.W. Hou, Z.Q. Ma, J. Phys. A: Math. Gen. 31, 7501 (1998); S.H. Dong, Z.Q. Ma, Phys. Rev. A. 65, 042717 (2002)

    Article  ADS  Google Scholar 

  14. S.H. Dong, X.W. Hou, Z.Q. Ma, Phys. Rev. A 58, 2160 (1998); X.Y. Gu, Z.Q. Ma, S.H. Dong, Phys. Rev. A 67, 062715 (2003); A. Calogeracos, N. Dombey, Phys. Rev. Lett. 93, 180405 (2004)

    Article  ADS  Google Scholar 

  15. S.H. Dong, X.W. Hou, Z.Q. Ma, Phys. Rev. A 59, 995 (1999); S.H. Dong, Eur. Phys. J. D 11, 159 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  16. M. Abramowitz, I.A. Stegun, Handbook of mathematical functions (Dover, New York 1965)

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-334, 09340, D. F., México

    Yu Jiang

  2. Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Lázaro Cárdenas 152, 07730, México, D. F., México

    Yu Jiang, Shi-Hai Dong & M. Lozada-Cassou

  3. Centro de Ciencias Físicas, UNAM, Apartado Postal 48-3, 62251, Cuernavaca, Morelos, México

    A. Antillón

Authors
  1. Yu Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shi-Hai Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Antillón
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Lozada-Cassou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Jiang.

Additional information

Arrival of the final proofs: 21 November 2005

PACS:

03.65.Ge, 03.65.-w, 11.80.-m

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, Y., Dong, SH., Antillón, A. et al. Low momentum scattering of the Dirac particlewith an asymmetric cusp potential. Eur. Phys. J. C 45, 525–528 (2006). https://doi.org/10.1140/epjc/s2005-02430-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2005-02430-7

Keywords

Search

Navigation