A PHASE-SPACE FLUCTUATION METHOD FOR QUANTUM DYNAMICS

A classical phase space method is developed to obtain connected graph representations of the Schrodinger propagator K(t, s, x, y) for quantum systems with arbitrary Hamiltonians. Re-statement of the original evolution problem in terms of variables describing fluctuations about a classical trajectory with endpoints x, t and y, s yields a family of new Hamiltonians that are perturbed (q, p)-quadratic operators. The Dyson series for this equivalent problem is summed exactly, by identifying the graph-combinatorial structure present in each order of perturbation theory and formally exponentiating the series. The coefficient functions in this cluster representation are classical transport integrals of phase space derivatives of the Weyl symbol of the perturbation, coupled by a Green function of the phase space Jacobi equation. An examination of the HBAR structure of log K results in a constructive (ansatz-free) derivation of the propagator's WKB expansion. (C) 1994 Academic Press, Inc.