Semiclassical Moyal quantum mechanics for atomic systems

The Moyal formalism utilizes the Wigner transform and associated Weyl calculus to define a phase-space representation of quantum mechanics. In this context, the Weyl symbol image of the Heisenberg evolution operator admits a generic semiclassical expansion that is based on classical transport and related [Formula Presented] quantum corrections. For two atom systems with a mutual pair interaction described by a spherically symmetric potential, the predictive power and convergence properties of this semiclassical expansion are investigated via numerical calculation. The rotational invariance and tensor structure present are used to simplify the semiclassical dynamics to the point where numerical computation in the six-dimensional phase space is feasible. For a variety of initial Gaussian wave functions and a selection of different observables, the [Formula Presented] and [Formula Presented] approximations for time dependent expectation 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 usefulness of Moyal quantum mechanics in the analysis of realistic atomic systems.