Virtual beams and the Klein paradox for the Klein-Gordon equation

Authors

  • A. Molgado Facultad de Ciencias, Universidad Autónoma de San Luis Potosí*, and Dual CP Institute of High Energy, México, *Lat. Av. Salvador Nava s/n. Col. Lomas, 78290, San Luis Potosí, México.
  • O. Morales Facultad de Ciencias, Universidad Autónoma de San Luis Potosí*, and Dual CP Institute of High Energy, México, *Lat. Av. Salvador Nava s/n. Col. Lomas, 78290, San Luis Potosí, México.
  • J.A. Vallejo Facultad de Ciencias, Universidad Autónoma de San Luis Potosí*, and Dual CP Institute of High Energy, México, *Lat. Av. Salvador Nava s/n. Col. Lomas, 78290, San Luis Potosí, México.

DOI:

https://doi.org/10.31349/RevMexFisE.64.1

Keywords:

Klein-Gordon equation, Klein paradox, Method of images.

Abstract

Whenever we consider any relativistic quantum wave equation we are confronted with the Klein paradox, which asserts that incident particles will suffer a surplus of reflection when dispersed by a discontinuous potential. Following recent results on the Dirac equation, we propose a solution to this paradox for the Klein-Gordon case by introducing virtual beams in a natural well-posed generalization of the method of images in the theory of partial differential equations. Thus, our solution considers a global reflection coefficient obtained from the two contributions, the reflected particles plus the incident virtual particles. Despite its simplicity, this method allows a reasonable understanding of the paradox within the context of the quantum relativistic theory of particles (according to the original setup for the Klein paradox) and without resorting to any quantum field theoretic issues.

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Published

2018-04-10