  Both the physical picture of the dynamics of atoms and molecules in intense
infrared fields and its theoretical description use the concept of electron
trajectories. Here we address a key question which arises in this context: Are
distinctly quantum features of these trajectories, such as the complex-valued
coordinates, physically relevant in the classically allowed region of phase
space, and what is their origin? First, we argue that solutions of classical
equations of motion can account for quantum effects. To this end, we construct
an exact solution to the classical Hamilton-Jacobi equation which accounts for
dynamics of the wave packet, and show that this solution is physically correct
in the limit $\hbar \to 0$. Second, we show that imaginary components of
classical trajectories are directly linked to the finite size of the initial
wavepacket in momentum space. This way, if the electronic wavepacket produced
by optical tunneling in strong infrared fiels is localised both in coordinate
and momentum, its motion after tunneling {\em ipso facto\/} cannot be described
with purely classical trajectories -- in contrast to popular models in the
literature.
