Causal Interpretation of Two-Dimensional Time-Dependent Scattering

This Demonstration studies a time-dependent collision of a two-dimensional wave packet with infinite wall barriers placed at right angles in the (, ) configuration space. In this case the analytic wavefunction is described by a product state:
for and , where and are standard one-dimensional free-particle solutions of the Schrödinger equation (SE) and where is a solution of the two-dimensional SE for free particles. In the causal interpretation of quantum theory (de Broglie–Bohm theory), the trajectories of the particles could be calculated from the phase of the total wavefunction. Contrary to the motion in (, ) space the trajectories can cross space-time points in the (, ) configuration space, as long as they do so at different times. Because of the product state of the wavefunction, the velocity in the direction is completely independent of the velocity in the direction. The graphic shows the particles, the whole paths of the particles, the squared wavefunction, and the infinite wall barriers (yellow).


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


R. W. Robinett, "Image Method Solutions for Free-Particle Wave Packets in Wedge Geometries," Eur. J. Phys., 27, 2006 pp. 281–289. Available online at arXiv:quant-ph/0512108v1 (2005).
    • 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+