  The difference between quantum isoenergetic process and quantum isothermal
process comes from the violation of the law of equipartition of energy in the
quantum regime. To reveal an important physical meaning of this fact, here we
study a special type of quantum heat engine consisting of three processes:
isoenergetic, isothermal and adiabatic processes. Therefore, this engine works
between the energy and heat baths. Combining two engines of this kind, it is
possible to realize the quantum Carnot engine. Furthermore, considering finite
velocity of change of the potential shape, here an infinite square well with
moving walls, the power output of the engine is discussed. It is found that the
efficiency and power output are both closely dependent on the initial and final
states of the quantum isothermal process. The performance of the engine cycle
is shown to be optimized by control of the occupation probability of the ground
state, which is determined by the temperature and the potential width. The
relation between the efficiency and power output is also discussed.
