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 energiesdepend 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 .

References

[1] 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.

[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." arxiv.org/pdf/quant-ph/0307035.pdf.