By the correspondence principle, the dynamics we have introduced via equation (2) must ensure that we recover Newtonian behavior for well-localized wave packets,
That this is true follows directly from Ehrenfest's theorem. Ehrenfest's theorem is a much stronger statement which holds exactly true for the time development of all quantum states (not just well-localized wave packets). Ehrenfest's theorem states
from which follows immediately the usual second order Newtonian equation of motion (9),
