Entropic uncertainty relation and revival structure of quantum wave packets

Abstract.

We consider a wave packet in the one-dimensional infinite square well formed by a combination of ground state and the first few excited states, and identify three different methods to study its time development. The first method proceeds by monitoring the temporal evolution of the so-called autocorrelation function while the second one relies on the behavior of standard deviation based Heisenberg’s position-momentum uncertainty relation as a function of time. The third method of our interest makes use of the time variation of the Shannon entropy sum or the so-called entropic uncertainty relation. The chosen form of the wave packet allowed us to study its revivals, super-revivals and fractional revivals by using analytic methods, the inevitable numerical routine being invoked at the last stage of the game. We found that, in general, the uncertainty-based approaches furnish more detailed information on the revival structure of wave packets than those provided by the autocorrelation function. The results of the entropic uncertainty relation, however, appear to be more accurate than the corresponding predictions of the standard deviation based uncertainty relation.