Scattering of a Klein-Gordon particle by a smooth barrier

Abstract

We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker $M_{\kappa ,\mu }(x)$ function. The reflection and transmission coefficients are calculated in terms of the energy, the height and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.

14 pages, 7 figures. Accepted in Can. J. Phys