  In the Dirac theory for the motion of free relativistic electrons, highly
oscillatory components appear in the time evolution of physical observables
such as position, velocity, and spin angular momentum. This effect is known as
zitterbewegung. We present a theoretical analysis of rather different
Hamiltonians with gapped and/or spin-split energy spectrum (including the
Rashba, Luttinger, and Kane Hamiltonians) that exhibit analogs of
zitterbewegung as a common feature. We find that the amplitude of oscillations
of the Heisenberg velocity operator v(t) generally equals the uncertainty for a
simultaneous measurement of two linearly independent components of v. It is
also shown that many features of zitterbewegung are shared by the simple and
well-known Landau Hamiltonian describing the dynamics of two-dimensional (2D)
electron systems in the presence of a magnetic field perpendicular to the
plane. Finally, we also discuss the oscillatory dynamics of 2D electrons
arising from the interplay of Rashba spin splitting and a perpendicular
magnetic field.
