Dynamics of uncertainties for bound one-dimensional semiclassical wave packets

We study the time evolution of the uncertainties Δx and Δp in position and momentum, respectively, associated with the semiclassical propagation of certain Gaussian initial states. We show that these quantities behave generically as |P₁(t) + tP₂(t)|, where P₁ and P are periodic in time with period that of an underlying classical trajectory. We also show that, despite the overall (generically quadratic) growth in time, the uncertainty product ΔxΔp achieves its minimum of h/2 at arbitrarily large times. Published by AIP Publishing.