  We consider a quantization of the Bianchi IX cosmological model based on
taking the constraint to be a self-adjoint operator in an auxiliary Hilbert
space. Using a WKB-style self-consistent approximation, the constraint chosen
is shown to have only continuous spectrum at zero. Nevertheless, the auxiliary
space induces an inner product on the zero-eigenvalue generalized eigenstates
such that the resulting physical Hilbert space has countably infinite
dimension. In addition, a complete set of gauge-invariant operators on the
physical space is constructed by integrating differential forms over the
spacetime. The behavior of these operators indicates that this quantization
preserves Wald's classical result that the Bianchi IX spacetimes expand to a
maximum volume and then recollapse.
