Thus, for large positive times, the uncertainty in X grows linearly, with the coefficient of t equal to ( Δ Δ ψ ψ 0 P ) / m . If the momentum of the initial wave function ψ ψ 0 is highly localized, the wave packet will spread slowly and the group-velocity approximation will remain good for a long time. Intuitively, this result says that if the initial wave function has a very sharply defined momentum, then the particle has a sharply defined velocity and will (to good approximation) propagate at this velocity for a long time.