Time-dependent tunneling of electron wave packets in a transverse magnetic field

We present a numerical study of the time-dependent tunneling of a Gaussian wave packet through a thick barrier in the presence of a transverse magnetic field. The time evolution of the charge density, current density, and total current are described in detail. The field dependence of the effective barrier transmission coefficient is studied and found to agree well with semiclassical results. The wave-packet center-of-mass delay time is found to decrease with increasing field strength and appears to tend to the zero-field phase-delay time.