标题： 半经典量子化三粒子扩展的Toda晶格；应用于Mixmaster各向异性哈密顿量 显示英文标题

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

摘要： 通常对3-Toda的量子化方法会导致需要许多步骤的数值计算，以确保其可靠性可能耗时较长。 为了尽可能减少EKB量子化程序中的数值部分，并简化数值计算，我们提出了使用更适合的变量重新构建数学框架。 由此得到的方程和程序可以轻松地用简短的Mathematica代码实现。 这种更明确的框架对于研究量子宇宙学中的Toda-Bianchi IX模型非常有用，在量子宇宙学中，真正的Bianchi IX各向异性哈密顿量可以用一个3粒子Toda系统来近似。 显示英文摘要

摘要： Usual approaches to quantisation of a 3-Toda lead to numerical calculations requiring many steps that can be time consuming to insure their reliability. In order to reduce as much as possible the numerical part of the EKB quantisation procedure, and then to ease numerical calculations, we propose a reformulation of the mathematical framework with more adapted variables. The resulting equations and procedure might be easily implemented in a short Mathematica code. This more explicit framework will be useful for studying quantum Toda-Bianchi IX models in quantum cosmology where the true Bianchi IX anisotropy Hamiltonian can be approximated by a 3-particle Toda system.