**Time evolution of a free wave packet
**Let Ψ(x,t) = (2π)

and assume that |g(k)| is centered at k

Let g(k) = |g(k)|exp(iα(k)). Then

Ψ(x,t) = (2π)

Here β(k) = α(k) - ω

If we again use the use a Taylor series expansion,

β(k) = β(k

then we already know that Ψ(x,t) peaks at

-dβ(k)/dk|

The peak of the wave packet moves with the

The velocity of a plane wave exp(i(kx - ωt) is v

ħω = ħ

A wave for which Δx << x and Δp << p can represent a classical particle moving with velocity v = v