  Egorov's theorem on the classical propagation of quantum observables is
related to prominent quasi-classical descriptions of quantum molecuar dynamics
as the linearized semiclassical initial value representation (LSC-IVR), the
Wigner phase space method or the statistical quasiclassical method. The error
estimates show that different accuracies are achievable for the computation of
expectation values and position densities. Numerical experiments for a Morse
model of diatomic iodine and confined Henon-Heiles systems in various
dimensions illustrate the theoretical results.
