Relativistic analysis of a wave packet interacting with a quantum-mechanical barrier

The dynamics of a wave packet incoming on a quantum-mechanical barrier is analyzed in the framework of a fully relativistic model, with particular emphasis on the case of a large spectrum. Some of the characteristic times of tunneling are calculated and compared; they are all of the same order of magnitude and all indicate an apparent superluminal motion, even if causality is maintained. A time-asymptotic expression for the transmitted wave function is derived and its strong validity is shown.