SEMICLASSICAL MOYAL QUANTUM-MECHANICS FOR ATOMIC SYSTEMS

The Moyal formalism utilizes' the Wigner transform and associated Weyl calc;ius to;define a phase-space representation of quantum mechanics. In this context, the Weyl symbol image of the Heisenberg evolution op erator admits a generic semiclassical expansion that is based on class ical transport and related O(h(2)) quantum corrections. For two atom s ystems with a mutual pair interaction described by a spherically symme tric potential, the predictive power and convergence properties of thi s semiclassical expansion are investigated via numerical calculation. The rotational invariance and tensor structure present are used to sim plify the semiclassical dynamics to the point where numerical computat ion in the six-dimensional phase space is feasible. For a variety of i nitial Gaussian wave functions and a selection of different observable s, the O(h(0)) and O(h(2)) approximations for time dependent expectati on values are determined. The interactions used are the Lennard-Jones potentials, which model helium, neon, and argon. The numerical results obtained provide a first demonstration of the practicality and useful ness of Moyal quantum mechanics in the analysis of realistic atomic sy stems. [S1050-2947(98)08110-4].