MIXING QUANTUM AND CLASSICAL MECHANICS

Quantum-classical mixing is studied by a group-theoretical approach, a nd a quantum-classical equation of motion is derived. The quantum-clas sical bracket entering the equation preserves the Lie algebra structur e of quantum and classical mechanics, and, therefore, leads to a natur al description of interaction between quantum and classical degrees of freedom. The exact formalism is applied to coupled quantum and classi cal oscillators. Various approximations, such as the mean-field and th e multiconfiguration mean-field approaches, which are of great utility in studying realistic multidimensional systems, are derived. Based on the formulation, a natural classification of the previously suggested quantum-classical equations of motion arises, and several problems fr om earlier works are resolved.