Particle in an Infinite Circular Well
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 .
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 .
 R. W. Robinett, "Visualizing the Solutions for the Circular Infinite Well in Quantum and Classical Mechanics," American Journal of Physics, 64(4), 1996 pp. 440–446.
 R. W. Robinett, Quantum Mechanics, Classical Results, Modern Systems and Visualized Examples, 2nd ed., Oxford: Oxford University Press, 2006.
 R. W. Robinett, "Quantum Mechanics of the Two-Dimensional Circular Billiard Plus Baffle System and Half-Integral Angular Momentum." arxiv.org/pdf/quant-ph/0307035.pdf.