Mixing Quantum and Classical Mechanics

Details Mixing Quantum and Classical Mechanics Mixing Quantum and Classical Mechanics

1996-10-11

arxiv.org/abs/quant-ph/9610016v1

Phys.Rev. A56 (1997) 162-176

Physics

Quantum Physics

31 pages, LaTeX2e

Scientific paper

10.1103/PhysRevA.56.162

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. We apply the formalism to coupled quantum and classical oscillators and show how various approximations, such as the mean-field and the multiconfiguration mean-field approaches, can be obtained from the quantum-classical equation of motion.

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