The time-dependent Dirac equation is solved numerically on a space-time gri
d for an atom in a strong static magnetic field and a laser field. The reso
nantly induced relativistic motion of the atomic electron leads to a ringli
ke spatial probability density similar to the features that have been recen
tly predicted [Wagner, Su, and Grobe, Phys. Rev. Lett. 84, 3282 (2000)] bas
ed on a phase-space method. We further demonstrate that spin-orbit coupling
for a fast-moving electron in such an atom becomes significant and the tim
e dependence of the spin can dephase even if initially aligned parallel to
the direction of the static magnetic field.