  We study spin-resolved probability distributions for electrons in a
multichannel waveguide in the presence of a spin-orbit interaction. For a
spin-polarized electron injection, a zitterbewegung pattern is predicted in the
probability distribution of electrons in the waveguide. For a spin-unpolarized
injection, the spin-resolved electron probability in the waveguide shows spin
accumulations. In addition to the spin Hall phenomenon, namely accumulations of
opposite spins at the lateral edges of the waveguide, we predict the existence
of a regular stripe pattern of spin accumulations in the internal region of the
waveguide. We show that the predicted zitterbewegung and spin Hall effect stem
from the same mechanism and are formed from coherent states of electrons in the
waveguide.
