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Time-Dependent Probability Density of Nonstationary States of an Electron in a Ring

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This Demonstration considers the probability density of nonstationary states of an electron of mass in a ring of radius . The wavefunction is given by

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,

which is a superposition of eigenstates, with and . The upper plot shows the probability density as a function of the angle (in radians). The lower diagram shows a polar plot of the probability density of the electron around the ring as a function of time . The color changes with the probability density, red indicating the highest density, and blue, the lowest.

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Contributed by: Valerie Greenwood, Rachel Kallianis and Anne Huetteman (May 8)
Open content licensed under CC BY-NC-SA

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References

[1] S. Montenegro and S. M. Blinder, "Particle on a Ring," LibreTexts Chemistry (Apr 11, 2023) chem.libretexts.org/Bookshelves/Physical_and_Theoretical _Chemistry _Textbook _Maps/Supplemental_Modules_ (Physical_and _Theoretical _Chemistry)/Quantum_Mechanics/05.5%3 A_Particle _in _Boxes/Particle_on_a _Ring.

[2] B. D. Anderson, "Cyclic Polyynes as Examples of the Quantum Mechanical Particle on a Ring," Journal of Chemical Education, 89(6), 2012 pp. 724–727. doi:10.1021/ed200439u.

[3] S. Stuart, Particle on a Ring [Video], YouTube. (Apr 11, 2023) www.youtube.com/watch?v=HOhhTfdDZt8.

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