Update 1_einstein_model.md - plot tweaks

src/1_einstein_model.md

@@ -254,7 +254,7 @@ ax.set_yticklabels(['$1$', '$2$'])
 draw_classic_axes(ax, xlabeloffset=.2)
 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.plot(temps, 1/2 + 1/(np.exp(1/temps)-1), '-', xline, yline, 'r--')
 ax2.set_ylim(bottom=0)
 ax2.set_xlabel('$k_B T$')
 ax2.set_xticks([0, 1])
@@ -263,6 +263,7 @@ ax2.set_ylabel(r"$\langle E \rangle$")
 ax2.set_yticks([1/2])
 ax2.set_yticklabels([r'$\hbar\omega_0/2$'])
 draw_classic_axes(ax2, xlabeloffset=.15)
+ax.text(1.05, 0.95, r'$k_{\rm B}T=\hbar \omega_0 =$', ha='left', color='r');
 ```
 
 We now calculate the heat capacity per atom $C$ explicitly. To do so, we need to differentiate $\langle E \rangle$ with respect to $T$.