  In many situations, one can approximate the behavior of a quantum system,
i.e. a wave function subject to a partial differential equation, by effective
classical equations which are ordinary differential equations. A general method
and geometrical picture is developed and shown to agree with effective action
results, commonly derived through path integration, for perturbations around a
harmonic oscillator ground state. The same methods are used to describe
dynamical coherent states, which in turn provide means to compute quantum
corrections to the symplectic structure of an effective system.
