Relation between quantum tunneling times for relativistic particles

A general relation between the phase time (group delay) and the dwell time is derived for relativistic tunneling particles described by the Dirac equation. It is shown that the phase time equals the dwell time plus a self-interference delay which is a relativistic generalization of previous results.

Figure 1

Phase time (solid curve), dwell time (dashed curve), and self-interference delay (dotted curve) versus normalized kinetic energy. Here $V_{0}L∕\hslash c=2\pi$ and $V_0∕m{c}^2=0.5$.

Figure 2

Phase time (solid curve), dwell time (dashed curve), and self-interference delay (dotted curve) versus normalized kinetic energy. (a) The nonrelativistic limit; here $V_{0}L∕\hslash c=2\pi$ and $V_0∕m{c}^2=0.001$. The relativistic limit; here $V_{0}L∕\hslash c=2\pi$ and $V_0∕m{c}^2=0.99$.