Klein's Paradox
arXiv:0712.0150 · doi:10.1016/S0375-9601(00)00833-1
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.
18 pages, Latex, another title has been used in the published version