  We consider the Dirac operator with a periodic potential on the half-line
with the Dirichlet boundary condition at zero. Its spectrum consists of an
absolutely continuous part plus at most one eigenvalue in each open gap. The
Dirac resolvent admits a meromorphic continuation onto a two-sheeted Riemann
surface with a unique simple pole on each open gap: on the first sheet (an
eigenvalue) or on the second sheet (a resonance). These poles are called states
and there are no other poles. If the potential is shifted by real parameter t,
then the continuous spectrum does not change but the states can change theirs
positions. We prove that each state is smooth and in general, non-monotonic
function of t. We prove that a state is a strictly monotone function of t for a
specific potential. Using these results we obtain formulas to recover
potentials of special forms.
