  We studied the expectation value of the scale factor in radiation and dust
quantum perfect fluid cosmology. We used Schutz variational formalism to
describe perfect fluid and selected the conjugate coordinate of perfect fluid
be dynamical variable. After quantization and solving the Wheeler-DeWitt
equation can obtain the exact solution. By superposition of the exact solution,
we obtained one wave packets and used it to compute the expectation value of
the scale factor. We found that if one select different dynamical variable be
the time variable in each of these two systems, the expectation value of the
scale factor of these two systems can fit in with the prediction of General
Relativity. Therefore we thought that the selection of reference time can be
different for different quantum perfect fluid systems.
