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We study the time evolution of the expectation value of the anharmonicoscillator coordinate in a coherent state as a toy model for understanding thesemiclassical solutions in quantum field theory. By using the deformationquantization techniques, we show that the coherent state expectation value canbe expanded in powers of $\hbar$ such that the zeroth-order term is a classicalsolution while the first-order correction is given as a phase-space Laplacianacting on the classical solution. This is then compared to the effective actionsolution for the one-dimensional $\f^4$ perturbative quantum field theory. Wefind an agreement up to the order $\l\hbar$, where $\l$ is the couplingconstant, while at the order $\l^2 \hbar$ there is a disagreement. Hence thecoherent state expectation values define an alternative semiclassical dynamicsto that of the effective action. The coherent state semiclassical trajectoriesare exactly computable and they can coincide with the effective actiontrajectories in the case of two-dimensional integrable field theories.Comment: 20 pages, no figure

Coherent states expectation values as semiclassical trajectories