Update 4_sommerfeld_model.md

src/4_sommerfeld_model.md

@@ -33,7 +33,30 @@ $$
 k_x=\frac{2\pi p}{L},\ k_y=\frac{2\pi q}{L},\ k_z=\frac{2\pi r}{L}\ \Rightarrow\ \varepsilon=\frac{2\pi^2\hbar^2}{mL^2}\left( p^2+q^2+r^2 \right)
 $$
 
-![](figures/free_electron.svg)
+```python
+kf = 3;
+extrapol = 1.2;
+ks = np.arange(-kf, kf+1);
+kcont = np.linspace(-extrapol*kf, extrapol*kf, 1000);
+
+Edis = ks**2;
+Econt = kcont**2;
+
+fig = plt.figure();
+ax = fig.add_subplot(111);
+ax.plot(kcont, Econt, 'b-');
+ax.plot(ks, Edis, 'k.');
+for i in range(2*kf + 1):
+    ax.plot([ks[i], ks[i]], [-0.75, Edis[i]], 'k:');
+ax.set_xlim(-3.75, 3.75);
+ax.set_ylim(-0.75, 11);
+
+ax.set_xlabel(r"$k \quad \left[ \frac{2 \pi}{L} \right]$");
+ax.set_ylabel(r"$\varepsilon$");
+
+ax.set_yticks([]);
+draw_classic_axes(ax, xlabeloffset=.2);
+```
 
 Comparable to phonons, but: electrons are _fermions_.