The exact correspondence between phase times and dwell times in a symmetrical quantum tunneling configuration

The general and explicit relation between phase times and dwell times for quantum tunneling or scattering is investigated. Considering two identical propagating wave packets symmetrically impinging a one-dimensional barrier, here we demonstrate that these two distinct transit time definitions give connected results where, for such a colliding configuration, the phase time (group delay) accurately describes the exact position of the scattered particles. The analytical difficulties that arise when the stationary phase method is employed for obtaining the phase (traversal) times are all overcome, since the multiple wave packet decomposition allows us to recover the exact position of the reflected and transmitted waves. In addition to the exact relation between the phase time and the dwell time, this leads to the right interpretation for both of them.