From a8d31faecc733fa4d63fde58ab98a5e9d11029c2 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 2 Apr 2023 16:57:12 +0200
Subject: Improve knowledge base

---
 .../know/concept/amplitude-rate-equations/index.md   | 20 ++++++++------------
 1 file changed, 8 insertions(+), 12 deletions(-)

(limited to 'source/know/concept/amplitude-rate-equations')

diff --git a/source/know/concept/amplitude-rate-equations/index.md b/source/know/concept/amplitude-rate-equations/index.md
index 0ca3248..d5eeb0d 100644
--- a/source/know/concept/amplitude-rate-equations/index.md
+++ b/source/know/concept/amplitude-rate-equations/index.md
@@ -9,21 +9,17 @@ layout: "concept"
 ---
 
 In quantum mechanics, the **amplitude rate equations** give
-the evolution of a quantum state's superposition coefficients through time.
-They are known as the precursors for
+the evolution of a quantum state in a time-varying potential.
+Although best known as the precursors of
 [time-dependent perturbation theory](/know/concept/time-dependent-perturbation-theory/),
-but by themselves they are exact and widely applicable.
+by themselves they are exact and widely applicable.
 
-Let $$\hat{H}_0$$ be a "simple" time-independent part
-of the full Hamiltonian,
-and $$\hat{H}_1$$ a time-varying other part,
-whose contribution need not be small:
+Let $$\hat{H}_0$$ be the time-independent part of the total Hamiltonian,
+and $$\hat{H}_1$$ the time-varying part
+(whose contribution need not be small),
+so $$\hat{H}(t) = \hat{H}_0 + \hat{H}_1(t)$$.
 
-$$\begin{aligned}
-    \hat{H}(t) = \hat{H}_0 + \hat{H}_1(t)
-\end{aligned}$$
-
-We assume that the time-independent problem
+Suppose that the time-independent problem
 $$\hat{H}_0 \Ket{n} = E_n \Ket{n}$$ has already been solved,
 such that its general solution is a superposition as follows:
 
-- 
cgit v1.2.3