From 059fb10d137f9dcda706672e227156a521679a3a Mon Sep 17 00:00:00 2001
From: "T. van der Sar" <t.vandersar@tudelft.nl>
Date: Mon, 10 Feb 2020 14:01:31 +0000
Subject: [PATCH] Update 1_einstein_model.md
---
src/1_einstein_model.md | 7 ++++---
1 file changed, 4 insertions(+), 3 deletions(-)
diff --git a/src/1_einstein_model.md b/src/1_einstein_model.md
index 5e249c00..bbb18d6f 100644
--- a/src/1_einstein_model.md
+++ b/src/1_einstein_model.md
@@ -226,7 +226,7 @@ This oscillator has an energy spectrum given by
$$\varepsilon_n=\left(n+\frac{1}{2}\right)\hbar\omega_0$$
where $\omega_0$ is the eigenfrequency of the oscillator.
-What is the thermal occupation and corresponding energy of this oscillator? A harmonic oscillator is a bosonic mode $\Rightarrow$ its occupation is described by the Bose-Einstein distribution:
+What is the thermal occupation and corresponding thermal energy stored in this oscillator? A harmonic oscillator is a bosonic mode $\Rightarrow$ its occupation is described by the Bose-Einstein distribution:
$$
n(\omega,T)=\frac{1}{ {\rm e}^{\hbar\omega/k_{\rm B}T}-1}
$$
@@ -234,8 +234,9 @@ The Bose-Einstein distribution describes the occupation probability of a state a
$$
\bar{\varepsilon}=\frac{1}{2}\hbar\omega_0+\frac{\hbar\omega_0}{ {\rm e}^{\hbar\omega_0/k_{\rm B}T}-1}
$$
-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.
-.
+
+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.
+
```python
fig, (ax, ax2) = pyplot.subplots(ncols=2, figsize=(10, 5))
omega = np.linspace(0.1, 2)
--
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