  In this work we study wave packet dynamics and $zitterbewegung$, an
oscillatory quantum motion, of heavy holes in III-V semiconductor quantum wells
in presence of a quantizing magnetic field. It is revealed that a Gaussian
wave-packet describing a heavy hole diffuses asymmetrically along the circular
orbit while performing cyclotron motion. The wave packet splits into two peaks
with unequal amplitudes after a certain time depending on spin-orbit coupling
constant. This unequal splitting of the wave packet is attributed to the cubic
Rashba interaction for heavy holes. The difference in the peak amplitudes
disappears with time. At a certain time the two peaks diffuse almost along the
entire cyclotron orbit. Then tail and head of the diffused wave packet
interfere and as a result a completely randomized pattern of the wave packet is
observed. The diffusion rate of the wave packet increases with increase of the
spin-orbit interaction strength. Also strong spin-orbit coupling expedite the
splitting and the randomization of the wave packet. We also study the
$zitterbewegung$ in various physical observables such as position, charge
current and spin angular momentum of the heavy hole. The $zitterbewegung$
oscillations are very much sensitive to the initial wave vector of the Gaussian
wave packet and the strength of the Rashba spin-orbit coupling.
