  We describe the quantum mechanical spreading of a Gaussian wave packet by
means of the semiclassical WKB approximation of Berry and Balazs. We find that
the time scale $\tau$ on which this approximation breaks down in a chaotic
system is larger than the Ehrenfest times considered previously. In one
dimension $\tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar)$, with $\lambda$ the Lyapunov
exponent and $A$ a typical classical action.
