Wave Packet Spreading in an Infinite Square Well

As a wave packet spreads in an infinite square well, it moves "back and forth" in a way similar to a classical trajectory.

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The solution of the Schrödinger equation ()
with boundary conditions is of the form
,
where is the length of the well and represents the initial wave packet with mean wavenumber and variance .
References
[1] I. Marzoli, F. Saif, I. Bialynicki-Birula, O. M. Friesch, A. E. Kaplan, and W. P. Schleich, "Quantum Carpets Made Simple." arXiv:quant-ph/9806033.
[2] R. C. O'Connell, "A Foray into Quantum Dynamics." arXiv:quant-ph/0212092.
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