  In this paper, we introduce an extension of the Dirac equation, very similar
to Dirac oscillator, that gives stationary localized wave packets as
eigenstates of the equation. The extension to the Dirac equation is achieved
through the replacement of the momentum operator by a PT-symmetric generalized
momentum operator. In the 1D case, the solutions represent bound particles
carrying spin having continuous energy spectrum, where the envelope parameter
defines the width of the packet without affecting the dispersion relation of
the original Dirac equation. In the 2D case, the solutions are localized wave
packets and are eigenstates of the third component of total angular momentum
and involve Bessel functions of integral order. In the 3D case, the solutions
are localized spherical wave packets with definite total angular momentum.
