The equations governing adiabatic and isothermal quantum processes involved
in an ideal two-state quantum heat engine are modified when the ideality r
estriction is removed. We seek and study a few situations to determine the
nature and magnitude of the modifications. If one confines such systems wel
l within the classical turning point, we show how one can profitably employ
the Wilson-Sommerfeld quantization rule to estimate the leading correction
terms due to non-ideality. The endeavour is likely to be important in stud
ies on practical quantum engines.