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Usual approaches to quantisation of a 3-Toda lead to numerical calculationsrequiring many steps that can be time consuming to insure their reliability. Inorder to reduce as much as possible the numerical part of the EKB quantisationprocedure, and then to ease numerical calculations, we propose a reformulationof the mathematical framework with more adapted variables. The resultingequations and procedure might be easily implemented in a short Mathematicacode. This more explicit framework will be useful for studying quantumToda-Bianchi IX models in quantum cosmology where the true Bianchi IXanisotropy Hamiltonian can be approximated by a 3-particle Toda system.

Semi-Classical quantisation of 3-particles Toda lattice augmented; Application to the Mixmaster anisotropy Hamiltonian