Solutions lecture 7

src/7_tight_binding_model_sol.md

@@ -4,7 +4,7 @@
 
 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
@@ -15,4 +15,4 @@ 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}
+Group velocity is given as $v=\hbar^-1 \frac{\partial E}{\partial k}$ with $E=\omega \hbar$.