Abstract: Dirac equation in an one dimensional bounded box with one moving wall is considered.
Instantaneous Hamiltonian is the standard self-adjoint Dirac Hamiltonian
but the time derivative in the Dirac equation is modified to guarantee the probability
conservation. The resulting equation is transformed to the Dirac equation in a static box
with time-dependent mass. Time-dependences of the average kinetic energy and quantum force
are analyzed, the average kinetic energy remains bounded for the box length bounded from below,
i.e., unlimited Fermi acceleration does not occur. The talk is based on the common paper with
D. Matrasulov and S. Rakhmanov, arXiv:2401.02837 [quant-ph]