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Fejer average and the short term behaviors of a wave packet in infinite square well

Quan-Hui Liu·Wei-Hong Qi·Li-Ping Fu·Bambi Hu
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Abstract

The first two period behaviors of a quantum wave packet in an infinite square well potential is studied. First, the short term behavior of expectation value of a quantity on an equally weighted wave packet (EWWP) is in classical limit proved to reproduce the Fej'{e}r average of the Fourier series decomposition of the corresponding classical quantity. Second, in order to best mimic the classical behavior, a nice relation between number $N$ of stationary states in the EWWP with the average quantum number $n$ as $N\thickapprox \sqrt{n}$ is revealed. Third, since the Fejér average can only approximate the classical quantity, it carries an uncertainty which in large quantum number case is almost the same as the quantum uncertainty.

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Quan-Hui Liu, Wei-Hong Qi, Li-Ping Fu, Bambi Hu. 2000-11-13. Fejer average and the short term behaviors of a wave packet in infinite square well. https://arxiv.org/abs/quant-ph/0011048

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