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authorPrefetch2022-12-17 18:19:26 +0100
committerPrefetch2022-12-17 18:20:50 +0100
commita39bb3b8aab1aeb4fceaedc54c756703819776c3 (patch)
treeb21ecb4677745fb8c275e54f2ad9d4c2e775a3d8 /source/know/concept/electric-dipole-approximation
parent49cc36648b489f7d1c75e1fde79f0990e08dd514 (diff)
Rewrite "Lagrange multiplier", various improvements
Diffstat (limited to 'source/know/concept/electric-dipole-approximation')
-rw-r--r--source/know/concept/electric-dipole-approximation/index.md4
1 files changed, 3 insertions, 1 deletions
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}