From aeacfca5aea5df7c107cf0c12e72ab5d496c96e1 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Tue, 3 Jan 2023 19:48:17 +0100
Subject: More improvements to knowledge base

---
 source/know/concept/rabi-oscillation/index.md | 21 ++++++++++-----------
 1 file changed, 10 insertions(+), 11 deletions(-)

(limited to 'source/know/concept/rabi-oscillation/index.md')

diff --git a/source/know/concept/rabi-oscillation/index.md b/source/know/concept/rabi-oscillation/index.md
index 2fcdea8..9497ad4 100644
--- a/source/know/concept/rabi-oscillation/index.md
+++ b/source/know/concept/rabi-oscillation/index.md
@@ -10,12 +10,12 @@ categories:
 layout: "concept"
 ---
 
-In quantum mechanics, from the derivation of
-[time-dependent perturbation theory](/know/concept/time-dependent-perturbation-theory/),
-we know that a time-dependent term $$\hat{H}_1$$ in the Hamiltonian
+In quantum mechanics, we know from the
+[amplitude rate equations](/know/concept/amplitude-rate-equations/)
+that a time-dependent term $$\hat{H}_1$$ in the Hamiltonian
 affects the state as follows,
 where $$c_n(t)$$ are the coefficients of the linear combination
-of basis states $$\Ket{n} e^{-i E_n t / \hbar}$$:
+of unperturbed basis states $$\ket{n} e^{-i E_n t / \hbar}$$:
 
 $$\begin{aligned}
     i \hbar \dv{c_m}{t}
@@ -24,10 +24,8 @@ $$\begin{aligned}
 
 Where $$\omega_{mn} \equiv (E_m \!-\! E_n) / \hbar$$
 for energies $$E_m$$ and $$E_n$$.
-Note that this equation is exact,
-despite being used for deriving perturbation theory.
-Consider a two-level system where $$n \in \{a, b\}$$,
-in which case the above equation can be expanded to the following:
+Consider a two-level system $$\{\ket{a}, \ket{b}\}$$ with $$E_a < E_b$$,
+in which case the above equation can be written out as:
 
 $$\begin{aligned}
     \dv{c_a}{t}
@@ -169,10 +167,11 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Note that the period was halved by squaring.
-This periodic "flopping" of the particle between $$\Ket{a}$$ and $$\Ket{b}$$
+This periodic "flopping" of the particle between $$\ket{a}$$ and $$\ket{b}$$
 is known as **Rabi oscillation**, **Rabi flopping** or the **Rabi cycle**.
 This is a more accurate treatment
-of the flopping found from first-order perturbation theory in textbooks.
+of the flopping found from first-order
+[time-dependent perturbation theory](/know/concept/time-dependent-perturbation-theory/).
 
 The name **generalized Rabi frequency** suggests
 that there is a non-general version.
@@ -205,7 +204,7 @@ $$\begin{aligned}
 
 Where $$\vec{E}_0$$ is the [electric field](/know/concept/electric-field/) amplitude,
 and $$\vec{d} \equiv q \matrixel{b}{\vec{r}}{a}$$ is the transition dipole moment
-of the electron between orbitals $$\Ket{a}$$ and $$\Ket{b}$$.
+of the electron between orbitals $$\ket{a}$$ and $$\ket{b}$$.
 Apparently, some authors define $$\vec{d}$$ with the opposite sign,
 thereby departing from its classical interpretation.
 
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