  We analyze the influence of relativistic effects on the minimum evolution
time between two orthogonal states of a quantum system. Defining the initial
state as an homogeneous superposition between two Hamiltonian eigenstates of an
electron in a uniform magnetic field, we obtain a relation between the minimum
evolution time and the displacement of the mean radial position of the electron
wavepacket. The quantum speed limit time is calculated for an electron dynamics
described by Dirac and Schroedinger-Pauli equations considering different
parameters, such as the strength of magnetic field and the linear momentum of
the electron in the axial direction. We highlight that when the electron
undergoes a region with extremely strong magnetic field the relativistic and
non-relativistic dynamics differ substantially, so that the description given
by Schroedinger-Pauli equation enables the electron traveling faster than c,
which is prohibited by Einstein's theory of relativity. This approach allows a
connection between the abstract Hilbert space and the space-time coordinates,
besides the identification of the most appropriate quantum dynamics used to
describe the electron motion.
