Ehrenfest's theorem : Classical Mechanics :: Schrodinger's wave equation : ?

Ehrenfest’s theorem shows that the average value of a quantum operator follows the same equations that govern a classical particle, just as Newton’s laws describe the motion of a classical body. In the same way, the Schrödinger wave equation supplies the rule that tells how a quantum state evolves over time. Thus the Schrödinger equation is to quantum dynamics what Newton’s laws (or Hamilton’s equations) are to classical dynamics. In other words, the Schrödinger equation plays the role of a “law of motion” for the wavefunction, just as Newton’s laws do for a particle’s trajectory. For example, the free‑particle Schrödinger equation predicts that the wave packet spreads, mirroring how a classical particle’s position changes under its momentum.