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1 files changed, 9 insertions, 7 deletions

diff --git a/content/know/concept/einstein-coefficients/index.pdc b/content/know/concept/einstein-coefficients/index.pdc
index 80707c6..9feaf8c 100644
--- a/content/know/concept/einstein-coefficients/index.pdc
+++ b/content/know/concept/einstein-coefficients/index.pdc
@@ -170,19 +170,21 @@ $$\begin{aligned}
     = \frac{\big|\!\matrixel{a}{H_1}{b}\!\big|^2}{\hbar^2} \frac{\sin^2\!\big( (\omega_{ba} - \omega) t / 2 \big)}{(\omega_{ba} - \omega)^2}
 \end{aligned}$$
 
-If the location of the nucleus of the atom has $z = 0$,
+If the nucleus is at $z = 0$,
 then generally $\ket{1}$ and $\ket{2}$ will be even or odd functions of $z$,
-such that $\matrixel{1}{z}{1} = \matrixel{2}{z}{2} = 0$, leading to:
+meaning that $\matrixel{1}{z}{1} = \matrixel{2}{z}{2} = 0$
+(see also [Laporte's selection rule](/know/concept/selection-rules/)),
+leading to:
 
 $$\begin{gathered}
-    \matrixel{1}{H_1}{2} = - E_0 d
+    \matrixel{1}{H_1}{2} = - E_0 d^*
     \qquad
-    \matrixel{2}{H_1}{1} = - E_0 d^*
+    \matrixel{2}{H_1}{1} = - E_0 d
     \\
     \matrixel{1}{H_1}{1} = \matrixel{2}{H_1}{2} = 0
 \end{gathered}$$
 
-Where $d \equiv q \matrixel{1}{z}{2}$ is a constant,
+Where $d \equiv q \matrixel{2}{z}{1}$ is a constant,
 namely the $z$-component of the **transition dipole moment**.
 The chance of an upward jump (i.e. absorption) is:
 
@@ -284,12 +286,12 @@ Let us return to the matrix elements of the perturbation $\hat{H}_1$,
 and define the polarization unit vector $\vec{n}$:
 
 $$\begin{aligned}
-    \matrixel{1}{\hat{H}_1}{2}
+    \matrixel{2}{\hat{H}_1}{1}
     = - \vec{d} \cdot \vec{E}_0
     = - E_0 (\vec{d} \cdot \vec{n})
 \end{aligned}$$
 
-Where $\vec{d} \equiv q \matrixel{1}{\vec{r}}{2}$ is
+Where $\vec{d} \equiv q \matrixel{2}{\vec{r}}{1}$ is
 the full **transition dipole moment** vector, which is usually complex.
 
 The goal is to calculate the average of $|\vec{d} \cdot \vec{n}|^2$.