The Airy Wave Train

Berry and Balazs [1] found a particular wavepacket in terms of an Airy function with the following properties:
1. It does not spread as it evolves in time.
2. It preserves its shape.
3. It accelerates, despite the fact that there are no apparent forces acting.

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DETAILS

The solution for the Airy packet is
,
where is an arbitrary positive constant, is the mass of the particle, and for simplicity, Planck's constant is taken as .
References
[1] M. V. Berry and N. L. Balazs, "Nonspreading Wavepackets," American Journal of Physics, 47(3), 1979 pp. 264–267. doi:10.1145/641876.641879.
[2] T. Curtright. "Time Dependent Wigner Functions." (Aug 7, 2013) server.physics.miami.edu/~curtright/TimeDependentWignerFunctions.html.
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