From 5cacf4ffaf3a9621ab536195f6469f98a420f054 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 5 Sep 2026 21:55:33 +0200
Subject: Improve knowledge base

---
 source/know/concept/multi-photon-absorption/index.md | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

(limited to 'source/know/concept/multi-photon-absorption')

diff --git a/source/know/concept/multi-photon-absorption/index.md b/source/know/concept/multi-photon-absorption/index.md
index 80dbc9b..481c19d 100644
--- a/source/know/concept/multi-photon-absorption/index.md
+++ b/source/know/concept/multi-photon-absorption/index.md
@@ -30,7 +30,6 @@ Here, we have made the
 to neglect the $$e^{i \omega t}$$ term,
 because it turns out to be irrelevant in this discussion.
 
-
 We call the ground state $$\Ket{0}$$,
 but other than that, the other states need *not* be sorted by energy.
 However, we demand that the following holds
@@ -187,7 +186,7 @@ i.e. for any odd-numbered final state $$\Ket{u}$$.
 ## Two-photon absorption
 
 Next, we go to second-order perturbation theory.
-Based on the previous result, this time
+Thanks to the previous result $$c_e^{(1)}(t) = 0$$, this time
 all odd-numbered states $$\Ket{u}$$ are unaffected:
 
 $$\begin{aligned}
@@ -248,7 +247,7 @@ two identical photons $$\hbar \omega$$ are absorbed simultaneously
 to bridge the energy gap $$\hbar \omega_{e0}$$.
 Surprisingly, such a transition can only occur when $$\matrixel{e}{\vu{p}}{0} = 0$$,
 i.e. for any even-numbered final state $$\Ket{e}$$.
-Notice that the rate is proportional to $$|\vb{E}|^4$$,
+The rate is proportional to $$|\vb{E}|^4$$,
 so this effect is only noticeable at high light intensities.
 
 
@@ -339,7 +338,7 @@ due to the dependence on $$\vb{E}$$.
 If $$N$$ is odd, only odd-numbered destinations $$\Ket{u}$$ are allowed
 (assuming the electron starts in the ground state $$\Ket{0}$$),
 and if $$N$$ is even, only even-numbered destinations $$\Ket{e}$$.
-Note that nothing has been said about the energies of these states
+Nothing has been said about the energies of these states
 (other than $$\Ket{0}$$ being the minimum);
 everything is determined by the matrix elements $$\matrixel{f}{\vu{p}}{i}$$.
 
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