Particle in an Infinite Circular Well

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration solves the quantum-mechanical problem of a particle confined to a disk, which can be called an infinite 2D circular well. The probability densities for several energy eigenstates are plotted. The azimuthal quantum number , equal to the number of angular nodes, determines the angular momentum . The radially excited state energies depend on the zeros of the Bessel function .

Contributed by: Enrique Zeleny (August 2013)
Based on a program by: Michael Trott
Open content licensed under CC BY-NC-SA



The solutions are of the form and with the quantized energy levels


where is the Planck constant, is the mass and is the zero of the Besssel function .


[1] R. W. Robinett, "Visualizing the Solutions for the Circular Infinite Well in Quantum and Classical Mechanics," American Journal of Physics, 64(4), \:200e1996 pp. 440–446.

[2] R. W. Robinett, Quantum Mechanics, Classical Results, Modern Systems and Visualized Examples, 2nd ed., Oxford: Oxford University Press, 2006.

[3] R. W. Robinett, "Quantum Mechanics of the Two-Dimensional Circular Billiard Plus Baffle System and Half-Integral Angular Momentum."

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.