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 .
[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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