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.

Automated summary

The study investigates the scattering behaviors of spin-0 and spin-1/2 particles interacting with one-dimensional energy-dependent barrier-type potentials using the Klein-Gordon and Dirac equations. It explores how different energy-dependent barrier-types affect the transmission and reflection coefficients of these particles, and points out Klein's paradox in the presence of energy-dependent step potential for spin-1/2 particles.