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), \: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." arxiv.org/pdf/quant-ph/0307035.pdf.
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