Update 1_einstein_model.md - polish

src/1_einstein_model.md

@@ -230,13 +230,12 @@ What is the thermal occupation and corresponding energy of this oscillator? A ha
 $$
 n(\omega,T)=\frac{1}{ {\rm e}^{\hbar\omega/k_{\rm B}T}-1}
 $$
-The Bose-Einstein distribution describes the occupation probability of a state at a given energy $\hbar \omega$. It is plotted as a function of energy below. We see that low-energy states are more likely to be occupied than high-energy states.  
-
-Using the Bose-Einstein distribution, we can calculate the expectation value of the energy stored in the oscillator  
+The Bose-Einstein distribution describes the occupation probability of a state at a given energy $\hbar \omega$. Using the Bose-Einstein distribution, we can calculate the expectation value of the energy stored in the oscillator  
 $$
 \bar{\varepsilon}=\frac{1}{2}\hbar\omega_0+\frac{\hbar\omega_0}{ {\rm e}^{\hbar\omega_0/k_{\rm B}T}-1}
 $$
-which we plot as a function of temperature below.  
+The plot on the left shows the Bose-Einstein distribution vs energy. We see that low-energy states are more likely to be occupied than high-energy states. The plot on the right shows the increasing thermal energy in the oscillator as a function of temperature and highlights the zero-point energy $\hbar\omega_0/2$ that remains in the oscillator at $T=0$, which is a consequence of the uncertainty principle.
+.   
 ```python
 fig, (ax, ax2) = pyplot.subplots(ncols=2, figsize=(10, 5))
 omega = np.linspace(0.1, 2)
@@ -262,7 +261,6 @@ ax2.set_yticklabels([r'$\hbar\omega/2$'])
 draw_classic_axes(ax2, xlabeloffset=.15)
 ```
 
-The term $\frac{1}{2}\hbar\omega_0$ is the _zero point energy_, which follows from the uncertainty principle.
 
 To calculate the heat capacity per atom $C$, we need to differentiate $\bar{\varepsilon}$ to $T$.
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