From 7c2d27ca89c5b096694b950c766e50df2dc87001 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sat, 8 Jan 2022 14:09:13 +0100
Subject: Minor fixes, rename "Ion Sound Wave" and "Ito Process"

---
 content/know/concept/time-dependent-perturbation-theory/index.pdc | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'content/know/concept/time-dependent-perturbation-theory/index.pdc')

diff --git a/content/know/concept/time-dependent-perturbation-theory/index.pdc b/content/know/concept/time-dependent-perturbation-theory/index.pdc
index 1fbd9ce..76ab684 100644
--- a/content/know/concept/time-dependent-perturbation-theory/index.pdc
+++ b/content/know/concept/time-dependent-perturbation-theory/index.pdc
@@ -59,13 +59,13 @@ We then take the inner product with an arbitrary stationary basis state $\ket{m}
 
 $$\begin{aligned}
     0
-    &= \sum_{n} \Big( \lambda c_n \matrixel{m}{\hat{H}_1}{n} - i \hbar \frac{d c_n}{dt} \braket{m}{n} \Big) \exp\!(- i E_n t / \hbar)
+    &= \sum_{n} \Big( \lambda c_n \matrixel{m}{\hat{H}_1}{n} - i \hbar \dv{c_n}{t} \braket{m}{n} \Big) \exp\!(- i E_n t / \hbar)
 \end{aligned}$$
 
 Thanks to orthonormality, this removes the latter term from the summation:
 
 $$\begin{aligned}
-    i \hbar \frac{d c_m}{dt} \exp\!(- i E_m t / \hbar)
+    i \hbar \dv{c_m}{t} \exp\!(- i E_m t / \hbar)
     &= \lambda \sum_{n} c_n \matrixel{m}{\hat{H}_1}{n} \exp\!(- i E_n t / \hbar)
 \end{aligned}$$
 
@@ -74,7 +74,7 @@ $\omega_{mn} \equiv (E_m - E_n) / \hbar$ to get:
 
 $$\begin{aligned}
     \boxed{
-        i \hbar \frac{d c_m}{dt}
+        i \hbar \dv{c_m}{t}
         = \lambda \sum_{n} c_n(t) \matrixel{m}{\hat{H}_1(t)}{n} \exp\!(i \omega_{mn} t)
     }
 \end{aligned}$$
-- 
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