Although we will have practically no occasion to use the quantum microcanonical ensemble (we relied on it more heavily in classical statistical mechanics), for completeness, we define it here. The function f, for this ensemble, is
where 
is the Heaviside step function. This says that
is 1 if 
and 0 otherwise. The
partition function for the ensemble is 
, since
the trace of 
is the number of members in the ensemble:
The thermodynamics that are derived from this partition function are exactly the same as they are in the classical case:
etc.