An impression of the dispersive behavior of this wave packet is obtained by looking at the probability density: | ψ ψ ( x , t ) | 2 = 2 / π π 1 + 4 t 2 e − − 2 ( x − − k 0 t ) 2 1 + 4 t 2 . It is evident that this dispersive wave packet, while moving with constant group velocity k o, is delocalizing rapidly: it has a width increasing with time as √ 1 + 4 t → 2 t, so eventually it diffuses to an unlimited region of space.