  We study the time required for a wave packet to tunnel beyond a square
barrier, or to be reflected, by envisaging a physical clock which ticks only
when the particle is within the barrier region. The clock consists in a
magnetic moment initially aligned with the $x$ axis which in the barrier region
precesses around a constant magnetic field aligned with the $z$ axis, the
motion being in the $y$ direction. The values of the $x$ and $y$ components of
the magnetic moment beyond or in front of the barrier allow to assign a
tunneling or reflection time to every fraction of the packet which emerges from
the barrier and to calculate tunneling times $\tau_{\rm T,x}$ and $\tau_{\rm
T,y}$ and reflection times $\tau_{\rm R,x}$ and $\tau_{\rm R,y}$. The times
$\tau_{\rm T,x}$ and $\tau_{\rm T,y}$ ($\tau_{\rm R,x}$ and $\tau_{\rm R,y}$)
are remarkably equal, and independent of the initial position (in front of the
barrier) of the packet.
