  The intrinsically relativistic problem of neutral fermions subject to
kink--like potentials ($\sim \mathrm{tanh} \gamma x$) is investigated and the
exact bound-state solutions are found. Apart from the lonely hump solutions for
$E=\pm mc^{2}$, the problem is mapped into the exactly solvable Surm-Liouville
problem with a modified P\"{o}schl-Teller potential. An apparent paradox
concerning the uncertainty principle is solved by resorting to the concepts of
effective mass and effective Compton wavelength.
