pythonize another two figures

src/7_tight_binding.md

@@ -69,7 +69,19 @@ The boundary conditions imply that in a system of size $L = Na$, we have $u_N =
 
 The following figure shows the interatomic potential with atoms placed at $x_k = ka$ with $k \in \mathbb{Z}$:
 
-![](figures/lattice_potential.svg)
+```python
+x = np.linspace(0.001, 3, 200)
+
+fig, ax = pyplot.subplots(1, 1)
+ax.plot(x, 1.2-1/np.abs(np.sin(np.pi * x))**(1/2))
+ax.set_ylim(-.7, .5)
+ax.set_xlabel("$x$")
+ax.set_ylabel("$U(x)$")
+ax.set_xticks([-.05, 1, 2])
+ax.set_xticklabels(["$0$", "$a$", "$2a$"])
+
+draw_classic_axes(ax)
+```
 
 Similarly to the triatomic system case, we formulate the molecular orbital via the LCAO model:
 $$
@@ -247,7 +259,20 @@ If we compare this to the dispersion relation $E=\hbar k^2/2m$ of the free elect
 
 Let us think what happens if we apply an external electric field to the crystal:
 
-![](figures/electric_field.svg)
+```python
+x = np.linspace(0.001, 3, 200)
+
+fig, ax = pyplot.subplots(1, 1)
+ax.plot(x, 1.2-1/np.abs(np.sin(np.pi * x))**(1/2) + .2 * (x - 1.5))
+ax.plot(x, .2 * (x - 0.25), '--')
+ax.set_ylim(-.7, .5)
+ax.set_xlabel("$x$")
+ax.set_ylabel("$U(x)$")
+ax.set_xticks([-.05, 1, 2])
+ax.set_xticklabels(["$0$", "$a$", "$2a$"])
+
+draw_classic_axes(ax)
+```
 
 The full Hamiltonian of the system is
 
@@ -368,7 +393,19 @@ What differences do you see?
 
 Consider electrons in a 1D atomic chain again:
 
-![](figures/lattice_potential.svg)
+```python
+x = np.linspace(0.001, 3, 200)
+
+fig, ax = pyplot.subplots(1, 1)
+ax.plot(x, 1.2-1/np.abs(np.sin(np.pi * x))**(1/2))
+ax.set_ylim(-.7, .5)
+ax.set_xlabel("$x$")
+ax.set_ylabel("$U(x)$")
+ax.set_xticks([-.05, 1, 2])
+ax.set_xticklabels(["$0$", "$a$", "$2a$"])
+
+draw_classic_axes(ax)
+```
 
 Let's expand the one-dimensional chain model by extending the range of the interaction further than the nearest neighbors: