The dispersion relation for a 1D Monoatomic chain is given by $$\omega = 2*\sqrt\frac{C}{M} \sin\left(\frac{qa}{2}\right)$$ We say that strong dispersion occurs when $q$ approaches $\frac{\pi}{a}$. Going by the literal meaning of dispersed, what exactly is begin strongly dispersed here? Or is there another specific meaning to the word "dispersed"?
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So the idea is that different plane waves will travel with different speeds $v=\lambda~f = k^{-1}\omega(k)$. A wave packet made of multiple of these would then be expected to disperse as one wave packet overtakes another.
Worth remembering that dispersion is not diffusion. The most common example is a Gaussian wave packet centered on some momentum $k_0$ which will travel as a Gaussian with speed $\mathrm d\omega/\mathrm d k$ without spreading out.
