The space-time evolution of electron and hole wave packets in different systems including 2D electron gas with
spin-orbit coupling, graphene and narrow gap semiconductors is considered. The electron probability densities and spin
densities are calculated and visualized. The nature of zitterbewegung oscillation is analyzed. In the presence of the
magnetic field oriented perpendicular to the 2D electron gas plane the wave packet splits into two parts, which rotate
with different cyclotron frequencies. The aim of investigations performed recently is not only a search of new applications
in spintronics, but also the prediction of new fundamental effects in physics of low dimensional structures.
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