Merge branch 'master' into local

src/1_einstein_model.md

@@ -235,7 +235,7 @@ $$
 \langle E \rangle=\frac{1}{2}\hbar\omega_0+\frac{\hbar\omega_0}{ {\rm e}^{\hbar\omega_0/k_{\rm B}T}-1}
 $$
 
-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). Moreover, we see that the energy in the oscillator is approximately constant when $kT<\hbar \omega_0$. I.e., the heat capacity becomes small for $kT<\hbar \omega_0$ and goes to zero when $T\rightarrow0$. 
+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). Moreover, we see that the energy in the oscillator is approximately constant when $k_{\rm B}T<\hbar \omega_0$. I.e., the heat capacity becomes small for $k_{\rm B}T<\hbar \omega_0$ and goes to zero when $T\rightarrow0$. 
 
 ```python
 xline = [1, 1];
@@ -247,12 +247,12 @@ ax.set_ylim(0, top=3)
 ax.set_xlim(left=0)
 ax.set_xlabel('$\hbar \omega$')
 ax.set_xticks([0, 1, 2])
-ax.set_xticklabels(['$0$', '$k_B T$'])
+ax.set_xticklabels(['$0$'])
 ax.set_ylabel('$n$')
 ax.set_yticks([1, 2])
 ax.set_yticklabels(['$1$', '$2$'])
 draw_classic_axes(ax, xlabeloffset=.2)
-ax.text(1, 1, r'$\hbar \omega = kT$', ha='left', color='r');
+ax.text(1.05, 0.95, r'$\hbar \omega = k_{\rm B}T$', ha='left', color='r');
 temps = np.linspace(0.01, 2)
 ax2.plot(temps, 1/2 + 1/(np.exp(1/temps)-1))
 ax2.set_ylim(bottom=0)