Time Evolution of the Wavefunction in a 1D Infinite Square Well

This Demonstration shows some solutions to the time-dependent Schrödinger equation for a 1D infinite square well. You can see how wavefunctions and probability densities evolve in time. You can set initial conditions as a linear combination of the first three energy eigenstates.


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


Vary the time to see the evolution of the wavefunction of a particle of mass in an infinite square well of length . Initial conditions are a linear combination of the first three energy eigenstates . The amplitude of each coefficient is set by the sliders. The phase of each coefficient at is set by the sliders. The wavefunction is automatically normalized.
Position is in units of .
is in units of .
is in units of .
Energy is in units of .
Time is in units of energy units).
    • 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+