= Physical meaning of a phonon
A <phonon> is one quantum of a crystal's vibrational <normal modes>. In the <harmonic approximation>, each mode is a quantum <harmonic oscillator> with <energy> levels $(n+1/2)\hbar\omega$. A <phonon> carries excitation <energy> $\hbar\omega$ and <crystal momentum> $\hbar q$ modulo a <reciprocal lattice> vector. It is a collective lattice excitation, not one atom travelling along the chain. <Phonons> obey <Bose-Einstein statistics>; their number need not be conserved in thermal equilibrium.
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