This linear growth is a reflection of the (time-invariant) momentum uncertainty: the wave packet is confined to a narrow Δ x = √ a /2, and so has a momentum which is uncertain (according to the uncertainty principle) by the amount ħ / √ 2 a, a spread in velocity of ħ/m √ 2 a, and thus in the future position by ħt /m √ 2 a. The uncertainty relation is then a strict inequality, very far from saturation, indeed! The initial uncertainty Δ x Δ p = ħ /2 has now increased by a factor of ħt/ma (for large t).