  The time-dependent Dirac equation is solved using the three-dimensional
Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave
packet in a vector potential is studied in the arrangements associated with the
Aharonov-Bohm effect. The solution of the Dirac equation showed a change in the
velocity of the electron wave packet even in a region where no forces acted on
the electron. The solution of the Dirac equation agreed with the prediction of
classical dynamics under the assumption that the dynamics was defined by the
conservation of generalized or canonical momentum. It was also shown that in
the case when the magnetic field was not zero, the conservation of generalized
or canonical momentum was equivalent to the action of the Lorentz force.
