A semiclassical approximation to quantum dynamics

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Abstract
In this paper we advance a new approximation scheme for the dynamics of an N particle system, which is based on the expansion of the Heisenberg equations of motion in powers of h/ in the coherent state representation. The time evolution of the physical observables is generated classically by a Hamiltonian Hs, which is derived from the original Hamiltonian by adding 2N2 virtual particles to the system. These virtual particles are related to the dispersion of the quantum mechanical wave function, and reflect the (time dependent) sensitivity of the instantaneous positions and momenta xi, pi to the variation of the initial conditions. The approximate equations of motion preserve the commutation relations between the coordinates and the momenta and the total (quantum) energy. The present approximation may be adequate for the study of the dynamics of coupled anharmonic oscillators in the quasiperiodic regime.