  For hole systems with an effective spin 3/2 we analyzed analytically and
numerically the evolution of wave packets with the different initial
polarizations. The dynamics of such systems is determined by the $4\times 4$
Luttinger Hamiltonian. We work in the space of arbitrary superposition of
light- and heavy-hole states of the "one-particle system". For 2D packets we
obtained the analytical solution for the components of wave function and
analyzed the space-time dependence of probability densities as well as angular
momentum densities. Depending on the value of the parameter $a=k_0d$ ($k_0$ is
the average momentum vector and $d$ is the packet width) two scenarios of
evolution are realized. For $a>>1$ the initial wave packet splits into two
parts and the coordinates of packet center experience the transient
oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the
case when $a<<1$ the distribution of probability density at $t>0$ remains
almost cylindrically symmetric and the ripples arise at the circumference of
wave packet. The ZB in this case is absent. We evaluated and visualized for
different values of parameter $a$ the space-time dependence of angular momentum
densities, which have the multipole structure. It was shown that the average
momentum components can precess in the absence of external or effective
magnetic fields due to the interference of the light- and heavy hole states.
For localized initial states this precession has a transient character.
