Solutions lecture 7

src/8_many_atoms_sol.md

@@ -57,11 +57,12 @@ The dispersion is given by: $$ E = \epsilon \pm \sqrt{t_1^2 + t_2^2 + 2t_1t_2\co
 ```python
 pyplot.figure()
 k = np.linspace(-2*pi, 2*pi, 300)
-pyplot.plot(k, np.sqrt(5+2*2*np.cos(k)),'b')
-pyplot.plot(k, -np.sqrt(5+2*2*np.cos(k)),'b')
-pyplot.plot(k, -3*np.cos(k/2),'r')
+pyplot.plot(k, np.sqrt(5+2*2*np.cos(k)),'b',label='2atom')
+pyplot.plot(k, -np.sqrt(5+2*2*np.cos(k)),'b',label='2atom')
+pyplot.plot(k, -3*np.cos(k/2),'r',label='1atom')
 pyplot.xlabel('$ka$'); pyplot.ylabel(r'$E-\epsilon$')
-pyplot.xticks([-pi, 0, pi], [r'$ka$', 0, r'$ka$'])
+pyplot.xticks([-2*pi, -pi, 0, pi,2*pi], [r'$-2ka$',r'$-ka$', 0, r'$ka$',r'$2ka$'])
 pyplot.yticks([-3, 0, 3], [r'$-t_1-t_2$', '$E_0$', r'$t_1+t_2$']);
+pyplot.legend([2atom,1atom],['2 atom unit cell dispersion','single atom unit cell dispersion'])
 ```