10217
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
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
.
RELATED LINKS
Airy Functions
Planck's Constant
(
ScienceWorld
)
Schrödinger Equation
(
ScienceWorld
)
PERMANENT CITATION
Enrique Zeleny
"
The Airy Wave Train
"
http://demonstrations.wolfram.com/TheAiryWaveTrain/
Wolfram Demonstrations Project
Published: August 14, 2013
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 »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Wave Packet Spreading in an Infinite Square Well
Enrique Zeleny
Laguerre-Gaussian Modes of Paraxial Wave Equation
Enrique Zeleny
Particle in an Infinite Circular Well
Enrique Zeleny
Bohm Trajectories for Quantum Airy Waves in a Time-Dependent Linear Potential
Klaus von Bloh
Wave Packets for Particle in a Box
Andrés Santos
Time Evolution of Optical Rogue Waves (Rogons) in the Causal Interpretation of Quantum Mechanics
Klaus von Bloh
Solution of a Nonlinear Schrödinger Equation
Enrique Zeleny
Spin-Weighted Spherical Harmonics
Satya Mohapatra
Spherical Harmonics
Stephen Wolfram
Plots of Quantum Probability Density Functions in the Hydrogen Atom
Carlos Rodríguez Fernández and Andrés Santos
Related Topics
Quantum Mechanics
Special Functions
Waves
Browse all topics
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+