  Closed-form, normalizable solutions of Dirac's equation propagating within a
semi-infinite cylindrical waveguide are obtained in terms of ordinary and
modified Bessel functions. These relativistic wave packets induce quantum
backflow on a cross-section of the cylinder at practically any distance along
the waveguide, becoming spin-polarized in the nonrelativistic limit. The
predicted backflow is stable in time and is manifest regardless of the initial
wave function.
