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.
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