  Analytic solutions of the quantum relativistic two-body problem are obtained
for an interaction potential modeled as a one-dimensional smooth square well.
Both stationary and moving pairs are considered and the limit of the
{\delta}-function interaction is studied in depth. Our result can be utilized
for understanding excitonic states in narrow-gap carbon nanotubes. We also show
the existence of bound states within the gap for a pair of particles of the
same charge.
