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We present a regularisation approach to the study of the quantum dynamics ofthe Mixmaster universe which allows to approximate the anisotropy potentialwith the explicitly integrable periodic 3-particle Toda system. This approachis based on a covariant Weyl-Heisenberg integral quantization. Such a procedurenaturally amplifies the dynamical role of the underlying Toda system bysmoothing out the three canyons of the anisotropy potential. Since therespective eigenfunctions can be explicitly constructed, our finding paves theway to a novel perturbative approach to the quantum Mixmaster dynamics.

Integrable Toda system as a quantum approximation to the anisotropy of Mixmaster