  We obtain an exact solution of the 1D Dirac equation for a square well
potential of depth greater then twice the particle's mass. The energy spectrum
formula in the Klein zone is surprisingly very simple and independent of the
depth of the well. This implies that the same solution is also valid for the
potential box (infinitely deep well). In the nonrelativistic limit, the
well-known energy spectrum of a particle in a box is obtained. We also provide
in tabular form the elements of the complete solution space of the problem for
all energies.
