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Peres has given us a clear and fully elaborated statement of the epistemology of quantum mechanics, and a rich source of examples of how ordinary questions can be posed in the theory,

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The classical limit of quantum mechanics is usually discussed in terms of Ehrenfest*s theorem, which states that, -for a sufficiently narrow wave packet, the mean position in the quantum state will follow a classical trajectory. We show, however, that that criterion is neither necessary nor sufficient to identify the classical regime. Generally speaking, the classical limit of a quantum state is not a single classical orbit, but an ensemble of orbits. The failure of the mean position in the quantum state to follow a classical orbit often merely reflects the fact that the centroid of a classical ensemble need not follow a classical orbit. A quantum state may behave essentially classically, even when Ehrenfest's theorem does not apply, if it yields agreement with the results calculated from the Liouville equation for a classical ensemble. We illustrate this fact with examples that include both regular and chaotic classical motions.PACS number(s): 03.65.Bz, 03.6S. Sq, 05.45. +b

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The equations of motion for phase-space moments and correlations are derived systematically for quantum and classical dynamics, and are solved numerically for chaotic and regular motions of the Hénon-Heiles model. For very narrow probability distributions, Ehrenfest's theorem implies that the centroid of the quantum state will approximately follow a classical trajectory. But the error in Ehrenfest's theorem does not scale with ប, and is found to be governed essentially by classical quantities. The difference between the centroids of the quantum and classical probability distributions, and the difference between the variances of those distributions, scale as ប 2 , and so are the true measures of quantum effects. For chaotic motions, these differences between quantum and classical motions grow exponentially, with a larger exponent than does the variance of the distributions. For regular motions, the variance of the distributions grows as t 2 , whereas the differences between the quantum and classical motions grow as t 3 . ͓S1050-2947͑98͒13009-3͔