  First a Friedmann-Robertson-Walker (FRW) universe filled with dust and a
conformally invariant scalar field is quantized. For the closed model we find a
discrete set of wormhole quantum states. In the case of flat spacelike sections
we find states with classical behaviour at small values of the scale factor and
quantum behaviour for large values of the scale factor. Next we study a FRW
model with a conformally invariant scalar field and a nonvanishing cosmological
constant dynamically introduced by regarding the vacuum as a perfect fluid. The
ensuing Wheeler-DeWitt equation turns out to be a bona fide Schrodinger
equation, and we find that there are realizable states with a definite value of
the cosmological constant. Once again we find finite-norm solutions to the
Wheeler-DeWitt equation with definite values of the cosmological constant that
represent wormholes, suggesting that in quantum cosmological models with a
simple matter content wormhole states are a common occurrence.
