English

Klein's Paradox

Quantum Physics 2007-12-04 v1

Abstract

We solve the one dimensional Feshbach-Villars equation for spin-1/2 particle subjected to a scalar smooth potential. The eight component wave function is given in terms of the hypergeometric functions and via a limiting procedure, the wave functions of the step potential are deduced. These wave functions are used to test the validity of the boundary conditions deduced from the Feshbach-Villars transformation. The creation of pairs is predicted from the boundary condition of the charge density.

Keywords

Cite

@article{arxiv.0712.0150,
  title  = {Klein's Paradox},
  author = {A. Bounames and L. Chetouani},
  journal= {arXiv preprint arXiv:0712.0150},
  year   = {2007}
}

Comments

18 pages, Latex, another title has been used in the published version

R2 v1 2026-06-21T09:49:32.245Z