Foundations of Physics

, Volume 44, Issue 9, pp 953–959 | Cite as

A Complete Proof of the Confinement Limit of One-Dimensional Dirac Particles

Article

Abstract

The validity of the confinement limit obtain by Unanyan et al. (Phys Rev A 79:044101, 2009) is extended by including non-symmetric vector and scalar potentials. It shows that the confinement limit of one-dimensional Dirac particles in vector and scalar potentials is \(\lambda _C/\sqrt{2}\), with \(\lambda _C\) being the Compton wavelength.

Keywords

Dirac equation Heisenberg uncertainty relation Confinement limit Compton wavelength 

References

  1. 1.
    Toyama, F.M., Nogami, Y.: Confinement limit of a Dirac particle in two and three dimensions. Phys. Lett. A 374, 3838 (2010)ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Unanyan, R.G., Otterbach, J., Fleischhauer, M.: Confinement limit of Dirac particles in scalar one-dimensional potentials. Phys. Rev. A 79, 044101 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    Toyama, F.M., Nogami, Y.: Confinement limit of the Dirac particle in one dimension. Phys. Rev. A 81, 044106 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Cheng, J.-Y.: More stringent confinement limit of the Dirac particle in one dimension. Phys. Rev. A 83, 054103 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    Thirring, W.: A soluble relativistic field theory. Ann. Phys. (N.Y.) 3, 91 (1958)ADSCrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Otterbach, J., Unanyan, R.G., Fleischhauer, M.: Confining stationary light: Dirac dynamics and Klein tunneling. Phys. Rev. Lett. 102, 063602 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    Fleischhauer, M., Otterbach, J., Unanyan, R.G.: Bose–Einstein condensation of stationary-light polaritons. Phys. Rev. Lett. 101, 163601 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    De Martino, A., Dell’Anna, L., Egger, R.: Magnetic confinement of massless Dirac fermions in graphene. Phys. Rev. Lett. 98, 066802 (2007)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Physics and Optoelectronic EngineeringGuangdong University of TechnologyGuangzhou China

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