Hint: Normal modes have the same function as $\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3$ have in $\mathbb{R}^3$.
Hint: The lectures concerns atom vibrations, so what will a phonon be?
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??? {Major Hint}
What's the question's title?
@@ -15,4 +16,4 @@ Hint: What kind of particles obey Bose-Einstein statistics? What kind of 'partic
2.
Group velocity is given as $v=\hbar^-1\frac{\partial E}{\partial k}$ with $E=\omega \hbar$.
Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ with $E=\omega \hbar$. So we find: $$v = \frac{a}{2}\sqrt{\frac{2\kappa}{m}}\frac{sin(ka){\sqrt{1-cos(ka)}}}
