  We investigate the quantum evolution of the universe in the presence of two
types of dark energies. First, we consider the phantom class ($\omega<-1$)
which would be responsible for a super-accelerated cosmic expansion, and then
we apply the procedure to an ordinary $\Lambda>0$ vacuum ($\omega=-1$). This is
done by analytically solving the Wheeler-DeWitt equation with ordering term
(WdW) in the cosmology of Friedmann-Robertson-Walker. In this paper, we find
exact solutions in the scale factor $a$ and the ordering parameter $q$. For
$q=1$ it is shown that the universe has a high probability of evolving from a
big bang singularity. On the other hand, for $q = 0$ the solution indicates
that an initial singularity is unlikely. Instead, the universe has maximal
probability of starting with a finite well-defined size which we compute
explicitly at primordial times. We also study the time evolution of the scale
factor by means of the Hamilton-Jacobi equation and show that an ultimate big
rip singularity emerges explicitly from our solutions. The phantom scenario
thus predicts a dramatic end in which the universe would reach an infinite
scale factor in a finite cosmological time as pointed by Caldwell et al. in a
classical setup. Finally, we solve the WdW equation with ordinary constant dark
energy and show that in this case the universe does not rip apart in a finite
era.
