Solutions lecture 7

src/7_tight_binding_model_sol.md

@@ -36,7 +36,8 @@ Group velocity is given as $v=\hbar^{-1}\frac{\partial E}{\partial k}$ with $E=\
 ```python
 pyplot.subplot(1,2,1)
 k = np.linspace(-pi+0.01, pi-0.01, 300)
-pyplot.plot(k, np.sin(k)/(np.sqrt(1-np.cos(k))));
+pyplot.plot(k[0:149], np.sin(k[0:149])/(np.sqrt(1-np.cos(k[0:149]))),'b');
+pyplot.plot(k[150:300], np.sin(k[150:300])/(np.sqrt(1-np.cos(k[150:300]))),'b');
 pyplot.xlabel('$k$'); pyplot.ylabel('$v(k)$');
 pyplot.xticks([-pi, 0, pi], [r'$-\pi/2$', 0, r'$\pi/2$']);
 pyplot.yticks([-np.sqrt(2), 0, np.sqrt(2)], [r'$-2\sqrt{\frac{\kappa}{m}}$', 0, r'$2\sqrt{\frac{\kappa}{m}}$']);
@@ -54,7 +55,7 @@ pyplot.tight_layout();
 
 ### Subquestion 4
 
-Hint: The group velocity is given as $v = \frac{d\omega}{dk}$, draw a coordinate system **under** or **above** the dispersion graph with $k$ on the x-axis in which you draw $\frac{d\omega}{dk}$.
+Hint: The group velocity is given as $v = \frac{d\omega}{dk}$, draw a coordinate system **under** or **above** the dispersion graph with $k$ on the x-axis in which you draw $\frac{d\omega}{dk}$. Draw a coordinate system **next** to the dispersion with *$g(\omega)$ on the y-axis*.
 
 ??? hint "Plot for density of states"