  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 fields of the
unperturbed solenoid acted on the electron. The solution of the Dirac equation
qualitatively agreed with the prediction of classical dynamics under the
assumption that the dynamics was defined by the conservation of generalized or
canonical momentum of the electron.
