  Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied.
Dirac equation with time-dependent boundary condition is mapped onto that with
static one, but with time-dependent mass. Exact analytical solution of such
modified Dirac equation is obtained for massless particle. For massive particle
the problem is solved numerically. Time-dependences of the main characteristics
of the dynamical confinement, such as average kinetic energy and quantum force
are analyzed. It is found that the average kinetic energy remains bounded for
the interval length bounded from below, in particular for the periodically
oscillating wall.
