The dynamic usage of the technique of effective potentials is motivated and established. The one-loop effective potential and the Gaussian effective potential are derived from Ehrenfrest's theorem by using adiabatic elimination. An application is made to the H\'enon-Heiles problem, and comparison is made with previous results; it is shown that quantum effects destroy chaos in two ways: (a) quantum fluctuations make the curvature more positive and (b) tunneling dominates the dynamics.
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Pattanayak et al. (1992) studied this question.
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