  We discuss the impact of a tiny Lorentz-violating $b^\mu$ term on the one
dimensional motion of a Dirac particle scattering on a rectangular barrier. We
assume the experiment is performed in a particular inertial frame, where the
components of $b^\mu$ are assumed constants. The results show that
Lorentz-violation modification to the transmission rate depends on the observer
Lorentz nature of $b^\mu$. For a spacelike or lightlike $b^\mu$ the induced
resonant frequency shift depends on the polarization, while for timelike
$b^\mu$ there is essentially no modification.
