Particle in an Infinite Circular Well

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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


Snapshots


Details

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.



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