Relativistic electron in a strong laser field: Quantum spreading

Following the previous post about a relativistic classical particle in a laser field, here we have the quantum version where the center of the wavepacket still follows the classical trajectory.

This movie corresponds to a weak relativistic electron interacting with a laser field. The laser wavelength is 800 nm with an intensity of 10^20 W/m^2. The propagation follows the  z direction. The electric field is polarized along the x direction where the oscillation is observed.

As we can clearly see, the wavepacket spreading is significant even in a single oscillation!  Of course, this information is absent in the classical model.

A second animation is shown below for a stronger laser field