Quantum Particles in an Infinite Square Potential Well

This Demonstration shows the probability of finding an electron in an infinite square potential well (top graphic) and also shows the wave function of the electron (bottom graphic).


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


quantum number — an integer value, one of the discrete quantum states of the electron
lower and upper limits — the lowest and highest x values for the position of the electron
The one-dimensional solution to Schrödinger's equation for an electron in an infinite square potential well (normalized to be of width 1) is , where is the quantum number. The square of this wave function is the probability density function for the electron.
The probability of finding the electron somewhere inside the square well is 1. (snapshot 1)
The probability of finding the electron with a quantum number of 3 between 0.2 and 0.8 is approximately 0.54. (snapshot 2)
The probability of finding the electron with a quantum number of 4 between 0.25 and 0.75 is approximately 0.5. (snapshot 3)
    • 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 © 2017 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+