  We study the effect of splitting and zitterbewegung of 1D and 2D electron
wave packets in the semiconductor quantum well under the influence of the
Rashba spin orbit coupling. Results of our investigations show that the spin
orbit interaction induces dramatic qualitative changes in the evolution of spin
polarized wave packet. The initial wave packet splits into two parts with
different spin polarization propagating with unequal group velocity. This
splitting appears due to the presence of two branches of electron spectrum
corresponding to the stationary states with different chirality. It is
demonstrated also that in the presence of external magnetic field B$
perpendicular to the electron gas plane the wave packet splits into two parts
which rotates with different cyclotron frequencies. It was shown that after
some periods the electron density distributes around cyclotron orbit and the
motion acquire an irregular character. Our calculations were made for both
cases of weak and strong spin orbit coupling.
