Solutions lecture 7

src/8_many_atoms_sol.md

@@ -55,7 +55,7 @@ $$
 The dispersion is given by: $$ E = \epsilon \pm \sqrt{t_1^2 + t_2^2 + 2t_1t_2\cos(ka)} $$
 
 ```python
-ppyplot.figure()
+pyplot.figure()
 k = np.linspace(-2*pi, 2*pi, 400)
 t1 = 1;
 t2 = 1.5;
@@ -66,9 +66,13 @@ pyplot.plot(k[199:100:-1],-(t1+t2)*np.cos(k[0:99]/2),'r--',label='1 atom dispers
 pyplot.plot(k[299:200:-1],-(t1+t2)*np.cos(k[300:399]/2),'r--')
 
 pyplot.xlabel('$ka$'); pyplot.ylabel(r'$E-\epsilon$')
-pyplot.xticks([-2*pi, -pi, 0, pi,2*pi], [r'$-2\pi',r'$-\pi$', 0, r'$\pi$',r'$2\pi$'])
-pyplot.yticks([-t1-t2, 0, t1+t2], [r'$-t_1-t_2$', 0, r'$t_1+t_2$']);
+pyplot.xlim([-2*pi,2*pi])
+pyplot,ylim([t1+t2,-(t1+t2)])
+pyplot.xticks([-2*pi, -pi, 0, pi,2*pi], [r'$-2ka$',r'$-ka$', 0, r'$ka$',r'$2ka$'])
+pyplot.yticks([-t1-t2, -np.abs(t1-t2), 0, np.abs(t1-t2), t1+t2], [r'$-t_1-t_2$',r'$-|t_1-t_2|$', '0', r'$|t_1-t_2|$', r'$t_1+t_2$']);
 pyplot.vlines([-pi, pi], -3, 3, linestyles='dashed');
+pyplot.hlines([-np.abs(t1-t2), np.abs(t1-t2)], -2*pi, 2*pi, linestyles='dashed');
+pyplot.fill_between([-3*pi,3*pi], -np.abs(t1-t2), np.abs(t1-t2), color='red',alpha=0.2);
 
 pyplot.legend(loc='lower center');
 ```