  We study the time evolution of a wave function for the spatially flat
Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt
equation in both analytical and numerical methods. We consider a Brown-Kuchar
dust as a matter field in order to introduce a "clock" in quantum cosmology and
adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits
an infinite number of self-adjoint extensions corresponding to a one-parameter
family of boundary conditions at the origin in the minisuperspace. For any
value of the extension parameter in the boundary condition, the evolution of a
wave function is unitary and the classical initial singularity is avoided and
replaced by the big bounce in the quantum system. Exact wave functions show
that the expectation value of the spatial volume of the universe obeys the
classical time evolution in the late time but its variance diverges.
