  The Dirac equation is solved for a pseudoscalar Coulomb potential in a
two-dimensional world. An infinite sequence of bounded solutions are obtained.
These results are in sharp contrast with those ones obtained in 3+1 dimensions
where no bound-state solutions are found. Next the general two-dimensional
problem for pseudoscalar power-law potentials is addressed consenting us to
conclude that a nonsingular potential leads to bounded solutions. The behaviour
of the upper and lower components of the Dirac spinor for a confining linear
potential nonconserving- as well as conserving-parity, even if the potential is
unbounded from below, is discussed in some detail.
