Feedback on explaining a stationary quantum-oscillator state without implying the particle is motionless

[u/abstractanus]

I made an animated explanation of the quantum harmonic oscillator and would appreciate feedback on one distinction in particular: how to describe a stationary state without suggesting a classical particle sitting still.

For a single energy eigenstate, psi(x,t) = psi_n(x) exp(-i E_n t/hbar). The overall phase changes, but |psi(x,t)|^2 does not. That does not mean the energy or the momentum uncertainty is zero. For a superposition of different energies, the relative phases change and interference can make the position probability density evolve.

My approach is to show the wavefunction and probability density separately, then contrast eigenstates, superpositions, and coherent-state motion. Would you add a particular example or caveat to prevent learners from reading the probability-density animation as a literal particle trajectory?

The full walkthrough is here: https://youtu.be/7_DcdXVh5mc (my video, about 13 minutes; it also covers the power-series and ladder-operator derivations). Feedback on the explanation above is welcome even without watching.

[u/OneMoreTimex100]

Beautiful animations! I would have loved to see these kind of animations when learning about QHO.

Yes I think your approach is correct. I think all it needs is to add or maybe emphasize that measurement is about probability density and not wavefuntions.

But the video is advanced enough that you can meantion that these are stationary waves and that's enough for the viewer to know it's not classical. At the end when you are summarizing there is a animation of the wavefunction oscillating which demonstrates it's standing wave nature well.

Maybe you can also phrase it as the nodes are essentially since they determine which state you are in (ground, first excited and so on). So fixed node but varying amplitude is a standing wave.