quantum mechanics - Reason for the Gaussian wave packet spreading

I have recently read how the Gaussian wave packet spreads while propagating. see: http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics

Though I understand the mathematics I don't understand the physical explanation behind it. Can you please explain?

Answer

The explanation is really very simple to understand intuitively, and very beautiful.

Imagine that a particle an uncertainity in its velocity $v$ of $\delta v$. Suppose at $t=0$ we have $x=x_{0}$. After $t=T$, the location of the particle will be given by the range $(x_{0}+Tv-T\delta v,x_{0}+Tv+T\delta v)$, because we dont know the exact velocity the particle started with. It evident that a probability of finding a particle has changed from being localised in the beginning to being diffused after some time: this is wave packet spreading.

Note that the range (wave packet size) increases with time monotonically, this means that even if we started with a diffused particle density for general case, it will just become much more diffused by extension of the arguement.