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 , where P1 and P2 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 ħ/2 at arbitrarily large times.
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Research Article| September 19 2016
Dynamics of uncertainties for bound one-dimensional semiclassical wave packets
Predrag Punoševac, Sam L. Robinson; Dynamics of uncertainties for bound one-dimensional semiclassical wave packets. J. Math. Phys. 1 September 2016; 57 (9): 092102. https://doi.org/10.1063/1.4962926
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