Ehrenfest’s Theorem — A Trajectory Becomes Blurred as Mass Decreases

A particle of mass m is thrown up from the origin with initial speed v₀ at angle θ. In classical mechanics it simply traces a parabola, but in quantum mechanics the wave packet spreads, so where it passes becomes blurred. Change the mass and see at what mass classical mechanics begins to hold.

In the uniform gravitational field V = mgy the Schrödinger equation can be solved exactly, so every wave packet on this page is an exact solution (no numerical approximation is used).