As a wave packet spreads in an infinite square well, it moves "back and forth" in a way similar to a classical trajectory.
The solution of the Schrödinger equation (
with boundary conditions
is of the form
is the length of the well and
represents the initial wave packet with mean wavenumber
 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.