  In this paper, we consider a model of two-level quantum heat engine to
investigate the explicit analytic expression for the thermodynamics quantities
in different condition under the finite-time operation. In this engine, the
working substance is composed of a spin-half particles immersed in a magnetic
field. The finite-time thermodynamic processes consisting of two quantum
adiabatic and two quantum isothermal processes. This processes working between
two heat reservoirs with an inverse temperatures $\beta_{1}$ and $\beta_{2}$
($<\beta_{1}$). In this processes, we obtain the work, heat, power and
efficiency at maximum power output of the model. Our result of the efficiency
at maximum power agree with the universal value in the first order of Carnot
efficiency.
