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A modified semi-classical method is used to construct both ground and excitedstate solutions to the canonically quantized vacuum Bianchi IX (Mixmaster)cosmological models. Employing a modified form of the semi-classical Ansatz wesolve the relevant Wheeler-DeWitt equation asymptotically by integrating a setof linear transport equations along the flow of a suitably chosen solution tothe corresponding Euclidean-signature Hamilton-Jacobi equation. For theMoncrief-Ryan (or `wormhole') Hamilton-Jacobi solution, we compute the groundstate quantum correction term associated with operator ordering ambiguities andshow how higher order correction terms can be computed. We also determine theexplicit, leading order forms of a family of excited states and show how tocompute their quantum corrections as smooth, globally defined functions on theBianchi IX minisuperspace. These excited-state solutions are peaked away fromthe minisuperspace origin and are labeled by a pair of positive integers thatcan be plausibly interpreted as graviton excitation numbers for the twoindependent anisotropy degrees of freedom. The modified semi-classical methodused here is applicable to more general models, representing a significantprogress in the Wheeler-DeWitt approach to quantum gravity.

Mixmaster Revisited: Wormhole Solutions to the Bianchi IX Wheeler-DeWitt Equation using the Euclidean-Signature Semi-Classical Method