Solutions lecture 7

src/7_tight_binding_model_sol.md

@@ -3,8 +3,16 @@
 ### Exercise 1: Lattice vibrations
 
 1.
-Hint: Normal modes have the same function as $$\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3$$ in $$\mathbb{R}^3$$.
+
+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?
 ??? Final Hint
 
     What's the question's title?
+
+Hint: What kind of particles obey Bose-Einstein statistics? What kind of 'particles' are phonons?
+
+2. 
+
+Group velocity is given as $v=\hbar^-1 \frac{\partial E}{\partial k}$ with $E=\omega \hbar$.