From 452c387b5311bd969f79ebec28925f2f1c8d3455 Mon Sep 17 00:00:00 2001
From: "T. van der Sar" <t.vandersar@tudelft.nl>
Date: Mon, 10 Feb 2020 13:53:29 +0000
Subject: [PATCH] Update 1_einstein_model.md - polish
---
src/1_einstein_model.md | 8 +++-----
1 file changed, 3 insertions(+), 5 deletions(-)
diff --git a/src/1_einstein_model.md b/src/1_einstein_model.md
index a7c37af7..787682cd 100644
--- a/src/1_einstein_model.md
+++ b/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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