From a39bb3b8aab1aeb4fceaedc54c756703819776c3 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 17 Dec 2022 18:19:26 +0100
Subject: Rewrite "Lagrange multiplier", various improvements

---
 source/know/concept/electric-dipole-approximation/index.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

(limited to 'source/know/concept/electric-dipole-approximation')

diff --git a/source/know/concept/electric-dipole-approximation/index.md b/source/know/concept/electric-dipole-approximation/index.md
index 7c710ec..35cf00c 100644
--- a/source/know/concept/electric-dipole-approximation/index.md
+++ b/source/know/concept/electric-dipole-approximation/index.md
@@ -30,6 +30,8 @@ so that $$\vb{A} \cdot \vu{P} = \vu{P} \cdot \vb{A}$$:
 
 $$\begin{aligned}
     \comm{\vb{A}}{\vu{P}} \psi
+    &= (\vb{A} \cdot \vu{P} - \vu{P} \cdot \vb{A}) \psi
+    \\
     &= -i \hbar \vb{A} \cdot (\nabla \psi) + i \hbar \nabla \cdot (\vb{A} \psi)
     \\
     &= i \hbar (\nabla \cdot \vb{A}) \psi
@@ -75,7 +77,7 @@ $$\begin{aligned}
 Where $$\vb{E}_0 = \omega \vb{A}_0$$.
 Let us restrict ourselves to visible light,
 whose wavelength $$2 \pi / |\vb{k}| \sim 10^{-6} \:\mathrm{m}$$.
-Meanwhile, an atomic orbital is several Bohr $$\sim 10^{-10} \:\mathrm{m}$$,
+Meanwhile, an atomic orbital is several Bohr radii $$\sim 10^{-10} \:\mathrm{m}$$,
 so $$\vb{k} \cdot \vb{x}$$ is negligible:
 
 $$\begin{aligned}
-- 
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