  The intrinsically relativistic problem of spinless particles subject to a
general mixing of vector and scalar kink-like potentials ($\sim \mathrm{tanh}
,\gamma x$) is investigated. The problem is mapped into the exactly solvable
Surm-Liouville problem with the Rosen-Morse potential and exact bounded
solutions for particles and antiparticles are found. The behaviour of the
spectrum is discussed in some detail. An apparent paradox concerning the
uncertainty principle is solved by recurring to the concept of effective
Compton wavelength.
