  For a FRW-spacetime coupled to an arbitrary real scalar field, we endow the
solution space of the associated Wheeler-DeWitt equation with a Hilbert-space
structure, construct the observables, and introduce the physical wave functions
of the universe that admit a genuine probabilistic interpretation. We also
discuss a proposal for the formulation of the dynamics. The approach to quantum
cosmology outlined in this article is based on the results obtained within the
theory of pseudo-Hermitian operators.
