Energy-dependent one-dimensional potentials and scattering of relativistic particles

Scattering behaviors of spin-0 and spin-1/2 particles interacting with one-dimensional energy-dependent barrier-type potentials are investigated by considering the Klein–Gordon and Dirac equations. The central question addressed by this study is how the energy-dependent barrier-type (rectangular, step, Hulthn, Woods–Saxon) characteristic affects the transmission and reflection coefficients of the Klein–Gordon and Dirac particles. Moreover, Klein’s paradox in the presence of energy-dependent step potential for the spin-1/2 particles is pointed out.