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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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 .
[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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+