Merge branch 'master' into local

src/1_einstein_model.md

@@ -235,16 +235,18 @@ $$
 \bar{\varepsilon}=\frac{1}{2}\hbar\omega_0+\frac{\hbar\omega_0}{ {\rm e}^{\hbar\omega_0/k_{\rm B}T}-1}
 $$
 
-The left plot shows the Bose-Einstein distribution vs energy. We see that low-energy states are more likely to be occupied than high-energy states. The right plot shows the increasing thermal energy in the oscillator for increasing temperature and highlights the zero-point energy $\hbar\omega_0/2$ that remains in the oscillator at $T=0$ - a consequence of the uncertainty principle.
+The left plot below shows the Bose-Einstein distribution vs energy. We see that low-energy states are more likely to be occupied than high-energy states. The right plot shows the increasing thermal energy in the oscillator for increasing temperature and highlights the zero-point energy $\hbar\omega_0/2$ that remains in the oscillator at $T=0$ - a consequence of the uncertainty principle.
 
 ```python
+xline = [1, 1];
+yline = [0, 2];
 fig, (ax, ax2) = pyplot.subplots(ncols=2, figsize=(10, 5))
 omega = np.linspace(0.1, 2)
-ax.plot(omega, 1/(np.exp(omega) - 1))
+ax.plot(omega, 1/(np.exp(omega) - 1), 'b', xline, yline, 'k')
 ax.set_ylim(0, top=3)
 ax.set_xlim(left=0)
-ax.set_xlabel(r'$\hbar \omega$')
-ax.set_xticks([0, 1])
+ax.set_xlabel('$\hbar \omega$')
+ax.set_xticks([0, 1, 2])
 ax.set_xticklabels(['$0$', '$k_B T$'])
 ax.set_ylabel('$n$')
 ax.set_yticks([1, 2])