Expand knowledge base, remove comments

1 files changed, 1 insertions, 4 deletions

diff --git a/content/know/concept/kubo-formula/index.pdc b/content/know/concept/kubo-formula/index.pdc
index f5430da..1df4780 100644
--- a/content/know/concept/kubo-formula/index.pdc
+++ b/content/know/concept/kubo-formula/index.pdc
@@ -5,6 +5,7 @@ publishDate: 2021-09-23
 categories:
 - Physics
 - Quantum mechanics
+- Perturbation
 
 date: 2021-09-23T16:21:51+02:00
 draft: false
@@ -54,9 +55,6 @@ $$\begin{aligned}
     &\approx \bigg( 1 + \frac{i}{\hbar} \int_{t_0}^t \hat{H}_{1,I}(t') \dd{t'} \bigg) \hat{A}_I(t)
     \bigg( 1 - \frac{i}{\hbar} \int_{t_0}^t \hat{H}_{1,I}(t') \dd{t'} \bigg)
     \\
-    %&= \bigg( \hat{A}_I + \frac{i}{\hbar} \int_{t_0}^t \hat{H}_{1,I}(t') \hat{A}_I \dd{t'} \bigg)
-    %\bigg( 1 - \frac{i}{\hbar} \int_{t_0}^t \hat{H}_{1,I}(t') \dd{t'} \bigg)
-    %\\
     &\approx \hat{A}_I(t)
     - \frac{i}{\hbar} \int_{t_0}^t \hat{A}_I(t) \hat{H}_{1,I}(t') \dd{t'}
     + \frac{i}{\hbar} \int_{t_0}^t \hat{H}_{1,I}(t') \hat{A}_I(t) \dd{t'}
@@ -102,7 +100,6 @@ describing the response of $\expval*{\hat{A}}$ to first order in $\hat{H}_1$:
 $$\begin{aligned}
     \boxed{
         \delta\expval*{\hat{A}}(t)
-        %= - \frac{i}{\hbar} \int_{t_0}^\infty \Theta(t \!-\! t') \expval{\comm{\hat{A}_I(t)}{\hat{H}_{1,I}(t')}}_0 \dd{t'}
         = \int_{t_0}^\infty C^R_{A H_1}(t, t') \dd{t'}
     }
 \end{aligned}$$