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Is it generally true that the wavepacket of a free particle spreads out as time goes to infinity? It seems like it would, since the phase velocities of the component plane waves are different, and therefore the plane waves would get increasingly out of phase with time. A gaussian wave packet spreads with time. I'm just wondering if it is true for arbitrary wavepackets, and if so, how do you show that?

thanks

edit: to be more specific, I'm trying to show that

[tex](\Delta x)^2 = \langle x^2 \rangle - \langle x \rangle ^2[/tex]

increases as t -> infinity

thanks

edit: to be more specific, I'm trying to show that

[tex](\Delta x)^2 = \langle x^2 \rangle - \langle x \rangle ^2[/tex]

increases as t -> infinity

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