Hermite-polynomial wavefunctions and coherent-state motion in the quantum oscillator
I made this animation of the quantum harmonic oscillator, including the connection between its derivations and the shapes of its states.
The mathematical structure is a Gaussian envelope multiplied by a Hermite polynomial. Normalizability selects the allowed energy levels, while ladder operators connect neighboring states. An individual energy eigenstate changes phase without changing its probability density; superpositions introduce interference, and a coherent state gives a localized packet whose center oscillates.
The video builds those ideas visually, starting from both the power-series and operator derivations. It assumes calculus and introductory quantum mechanics; the full explanation is about 13 minutes.
u/abstractanus — 8 days ago