Solutions lecture 7

src/7_tight_binding_model_sol.md

@@ -16,4 +16,4 @@ Hint: What kind of particles obey Bose-Einstein statistics? What kind of 'partic
 
 2. 
 
-Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ and $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$ with $E=\omega \hbar$. So we find: $$ v(k) = \frac{a}{2}\sqrt{\frac{2\kappa}{m}}\frac{sin(ka)}{\sqrt{1-cos(ka)}}$$ $$ g(k) = \frac{L}{2\pi}$$
+Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ and $g(\omega) = \frac{dN}{d\omega} = \frac{dN}{dk}\frac{dk}{d\omega}$ with $E=\omega \hbar$. So we find: $$ v(k) = \frac{a}{2}\sqrt{\frac{2\kappa}{m}}\frac{\sin(ka)}{\sqrt{1-\cos(ka)}}$$ $$ g(k) = \frac{L}{2\pi}$$