  We present an optimal analysis for a quantum mechanical engine working
between two energy baths within the framework of relativistic quantum
mechanics, adopting a first-order correction. This quantum mechanical engine,
with the direct energy leakage between the energy baths, consists of two
adiabatic and two isoenergetic processes and uses a three-level system of two
non-interacting fermions as its working substance. Assuming that the potential
wall moves at a finite speed, we derive the expression of power output and, in
particular, reproduce the expression for the efficiency at maximum power.
