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Considering the free evolution of a Gaussian wave packet, is it possible to use Ehrenfest's theorem to determine the average value of momentum given that of position?

And I imply the simplified version of the theorem, namely $\frac{\mathrm d}{\mathrm d t}\langle x \rangle = \frac{1}{m}\langle p \rangle$, where $x$ and $p$ are the position and momentum, respectively.

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    $\begingroup$ Yes. Ehrenfest theorem is a general theorem which does not depend on the shape of the wavefunction. See its application to the operator position $X$ in Wiki. $\endgroup$
    – Trimok
    Commented Oct 24, 2013 at 9:30

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Yes, you can apply the Ehrenfest's theorem to determine the expectation value of momentum for a given position or to determine the expectation value of position for a given momentum for a Gaussian wave packet!

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