Time-Dependent Probability Density of Nonstationary States of an Electron in a Ring
This Demonstration considers the probability density of nonstationary states of an electron of mass in a ring of radius . The wavefunction is given by[more]
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.[less]
 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.
 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.
 S. Stuart, Particle on a Ring [Video], YouTube. (Apr 11, 2023) www.youtube.com/watch?v=HOhhTfdDZt8.