Expand knowledge base, remove comments

1 files changed, 0 insertions, 9 deletions

diff --git a/content/know/concept/selection-rules/index.pdc b/content/know/concept/selection-rules/index.pdc
index 22dfd64..9fda878 100644
--- a/content/know/concept/selection-rules/index.pdc
+++ b/content/know/concept/selection-rules/index.pdc
@@ -304,10 +304,6 @@ By inserting the expressions we found earlier for these commutators, we get:
 
 $$\begin{aligned}
     \comm*{\hat{L}^2}{\comm*{\hat{L}^2}{\hat{x}}}
-    %&= - 2 \hbar^2 \big( 2 (\hat{z} \hat{L}_x - \hat{x} \hat{L}_z - i \hbar \hat{y}) \hat{L}_z
-    %- 2 (\hat{x} \hat{L}_y - \hat{y} \hat{L}_x - i \hbar \hat{z}) \hat{L}_y
-    %- (\hat{L}^2 \hat{x} - \hat{x} \hat{L}^2) \big)
-    %\\
     &= - 4 \hbar^2 \big( \hat{z} \hat{L}_x \hat{L}_z - \hat{x} \hat{L}_z^2  - i \hbar \hat{y} \hat{L}_z
     + \hat{y} \hat{L}_x \hat{L}_y - \hat{x} \hat{L}_y^2 + i \hbar \hat{z} \hat{L}_y \big) \\
     &\qquad\qquad + 2 \hbar^2 \big( \hat{L}^2 \hat{x} - \hat{x} \hat{L}^2 \big)
@@ -334,10 +330,6 @@ which we use to arrive at:
 
 $$\begin{aligned}
     \comm*{\hat{L}^2}{\comm*{\hat{L}^2}{\hat{x}}}
-    %&= - 4 \hbar^2 \big( \hat{z} \hat{L}_z \hat{L}_x + \hat{y} \hat{L}_y \hat{L}_x + \hat{x} \hat{L}_x^2
-    %- \hat{x} \hat{L}_x^2 - \hat{x} \hat{L}_y^2 - \hat{x} \hat{L}_z^2 \big)
-    %+ 2 \hbar^2 \big( \hat{L}^2 \hat{x} - \hat{x} \hat{L}^2 \big)
-    %\\
     &= - 4 \hbar^2 \big( \hat{z} \hat{L}_z \hat{L}_x + \hat{y} \hat{L}_y \hat{L}_x + \hat{x} \hat{L}_x^2 - \hat{x} \hat{L}^2 \big)
     + 2 \hbar^2 \big( \hat{L}^2 \hat{x} - \hat{x} \hat{L}^2 \big)
     \\
@@ -386,7 +378,6 @@ so the right-hand side becomes:
 
 $$\begin{aligned}
     2 \hbar^2 \matrixel{f}{\vu{r} \hat{L}^2 \!\!+\! \hat{L}^2 \!\vu{r}}{i}
-    %\matrixel{\ell_f m_f}{\comm*{\hat{L}^2}{\comm*{\hat{L}^2}{\vu{r}}}}{\ell_i m_i}
     &= 2 \hbar^2 \big( \matrixel{f}{\vu{r} \hat{L}^2}{i} + \matrixel{f}{\hat{L}^2 \vu{r}}{i} \big)
     \\
     &= 2 \hbar^2 \big( \hbar^2 \ell_i (\ell_i \!+\! 1) \matrixel{f}{\vu{r}}{i}