From 075683cdf4588fe16f41d9f7b46b9720b42b2553 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Wed, 17 Jul 2024 10:01:43 +0200
Subject: Improve knowledge base

---
 source/know/concept/laser-rate-equations/index.md | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'source/know/concept/laser-rate-equations/index.md')

diff --git a/source/know/concept/laser-rate-equations/index.md b/source/know/concept/laser-rate-equations/index.md
index c81f02b..feec168 100644
--- a/source/know/concept/laser-rate-equations/index.md
+++ b/source/know/concept/laser-rate-equations/index.md
@@ -30,7 +30,7 @@ $$\begin{aligned}
 
 Where $$n$$ is the background medium's refractive index,
 $$\omega_0$$ the two-level system's gap resonance frequency,
-$$|g| \equiv |\matrixel{e}{\vu{x}}{g}|$$ the transition dipole moment,
+$$|g| \equiv |\!\matrixel{e}{\vu{x}}{g}\!|$$ the transition dipole moment,
 $$\gamma_\perp$$ and $$\gamma_\parallel$$ empirical decay rates,
 and $$D_0$$ the equilibrium inversion.
 Note that $$\vb{E}^{-} = (\vb{E}^{+})^*$$.
@@ -110,7 +110,7 @@ $$\begin{aligned}
 
 Where the Lorentzian gain curve $$\gamma(\omega)$$
 (which also appears in the [SALT equation](/know/concept/salt-equation/))
-represents a laser's preferred spectrum for amplification,
+represents the laser's preferred spectrum for amplification,
 and is defined like so:
 
 $$\begin{aligned}
@@ -139,7 +139,7 @@ $$\begin{aligned}
 
 Next, we insert our ansatz for $$\vb{E}^{+}$$ and $$\vb{P}^{+}$$
 into the third MBE, and rewrite $$\vb{P}_0^{+}$$ as above.
-Using our identity for $$\gamma(\omega)$$,
+Using the aforementioned identity for $$\gamma(\omega)$$
 and the fact that $$\vb{E}_0^{+} \cdot \vb{E}_0^{-} = |\vb{E}|^2$$, we find:
 
 $$\begin{aligned}
@@ -218,8 +218,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Where $$\gamma_e$$ is a redefinition of $$\gamma_\parallel$$
-depending on the electron decay processes,
-and the photon loss rate $$\gamma_p$$, the gain $$G$$,
+depending on the electron decay processes.
+The photon loss rate $$\gamma_p$$, the gain $$G$$,
 and the carrier supply rate $$R_\mathrm{pump}$$
 are defined like so:
 
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