The Airy Wave Train
Berry and Balazs  found a particular wavepacket in terms of an Airy function with the following properties:[more]
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.[less]
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 .
 M. V. Berry and N. L. Balazs, "Nonspreading Wavepackets," American Journal of Physics, 47(3), 1979 pp. 264–267. doi:10.1145/641876.641879.
 T. Curtright. "Time Dependent Wigner Functions." (Aug 7, 2013) server.physics.miami.edu/~curtright/TimeDependentWignerFunctions.html.