From 3170fc4b5c915669cf209a521e551115a9bd0809 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Wed, 20 Oct 2021 11:50:20 +0200
Subject: Expand knowledge base

---
 content/know/concept/maxwell-bloch-equations/index.pdc | 15 ++++++++++++---
 1 file changed, 12 insertions(+), 3 deletions(-)

(limited to 'content/know/concept/maxwell-bloch-equations/index.pdc')

diff --git a/content/know/concept/maxwell-bloch-equations/index.pdc b/content/know/concept/maxwell-bloch-equations/index.pdc
index ae7d119..020a120 100644
--- a/content/know/concept/maxwell-bloch-equations/index.pdc
+++ b/content/know/concept/maxwell-bloch-equations/index.pdc
@@ -393,9 +393,18 @@ It is trivial to show that $\vb{E}$ and $\vb{P}$
 can be replaced by $\vb{E}^{+}$ and $\vb{P}^{+}$.
 It is also simple to convert
 the dipole $\vb{p}^{+}$ and inversion $d$
-into their macroscopic versions $\vb{P}^{+}$ and $D$,
-simply by averaging over the atoms per unit of volume.
-We thus arrive at the **Maxwell-Bloch equations**:
+into their macroscopic versions $\vb{P}^{+}$ and $D$:
+
+$$\begin{aligned}
+    \vb{P}^{+}(\vb{r}, t)
+    = \sum_{n} \vb{p}^{+}_n \: \delta(\vb{r} \!-\! \vb{r}_n)
+    \qquad \quad
+    D(\vb{r}, t)
+    = \sum_{n} d_n \: \delta(\vb{r} \!-\! \vb{r}_n)
+\end{aligned}$$
+
+We thus arrive at the **Maxwell-Bloch equations**,
+which are relevant for laser theory:
 
 $$\begin{aligned}
     \boxed{
-- 
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