Theory Notes - Revision history

Drake: /* Matrix Elements of H */

2024-09-23T00:51:35Z

‎Matrix Elements of H

2021-03-12T01:48:19Z

‎General Hermitian Property

2020-12-14T16:09:11Z

2020-12-14T05:36:59Z

‎General Hermitian Property

2020-12-14T05:34:16Z

‎General Hermitian Property

2020-12-14T05:30:51Z

‎General Hermitian Property

2020-12-14T05:25:57Z

Undo revision 800 by Drake (talk)

2020-12-14T05:25:03Z

‎General Hermitian Property

2020-12-14T05:21:56Z

Undo revision 798 by Drake (talk)

2020-12-14T05:19:06Z

‎General Hermitian Property

@@ Line 836: / Line 836: @@
 \begin{equation}
-\nabla^2_1 \mathcal{F} = \left\{ \frac{1}{r_1^2} \left[ a \left( a + 1 \right) - l_1 \left( l_1 + 1 \right) \right] + \frac{c \left( c + 1 \right)}{r^2} + \alpha^2\frac{2\alpha \left( a + 1 \right)}{r_1} + \frac{2 \left(r_1 - r_2 \cos \theta \right) }{r_1r^2}c \left[ a - \alpha r_1 \right] - \frac{2c}{r^2} \left( \hat{\nabla}^Y_1 \cdot \hat{r}_2 \right) \frac{r_2}{r_1} \right\} \mathcal{F}
+\nabla^2_1 \mathcal{F} = \left\{ \frac{1}{r_1^2} \left[ a \left( a + 1 \right) - l_1 \left( l_1 + 1 \right) \right] + \frac{c \left( c + 1 \right)}{r^2} + \alpha^2 + \frac{2\alpha \left( a + 1 \right)}{r_1} + \frac{2 \left(r_1 - r_2 \cos \theta \right) }{r_1r^2}c \left( a - \alpha r_1 \right) - \frac{2c}{r^2} \left( \hat{\nabla}^Y_1 \cdot \hat{r}_2 \right) \frac{r_2}{r_1} \right\} \mathcal{F}
 \end{equation}

@@ Line 1,097: / Line 1,097: @@
 <math>
-D_1 = -1(1-x)\alpha_+^2 +\alpha_-^2 - 2\frac{c_-}{c_+}\alpha_-\alpha_+
+D_1 = -(1-x)\alpha_+^2 +\alpha_-^2 - 2\frac{c_-}{c_+}\alpha_-\alpha_+
 </math>

← Older revision		Revision as of 16:09, 14 December 2020
Line 1,470:		Line 1,470:
	\end{equation}		\end{equation}
	is the absorption oscillator strength.		is the absorption oscillator strength.
−
−	~~===Test===~~
−	~~This is a test edit~~

@@ Line 1,008: / Line 1,008: @@
 Subtracting gives
 \begin{eqnarray*}
-f_8(Y)-f_8(Y^\prime)=-\frac{1}{2}[a_+f_6\nabla^-_1+b_+f_7\nabla_2^-]\tag{IV}\\
+f_8(Y)-f_8(Y^\prime)&=&-\frac{1}{2}[a_+f_6\nabla^-_1+b_+f_7\nabla_2^-]\tag{IV}\\
-a[-2a_+f_1-2f_2-b_+f_3-f_6\nabla^+_1]=0\tag{V}\\
+a[-2a_+f_1-2f_2-b_+f_3-f_6\nabla^+_1]&=&0\tag{V}\\
-b[-2b_+f_4-2f_5-a_+f_3-f_7\nabla^+_2]=0\tag{VI}\\
+b[-2b_+f_4-2f_5-a_+f_3-f_7\nabla^+_2]&=&0\tag{VI}\\
 \end{eqnarray*}

@@ Line 1,007: / Line 1,007: @@
 Subtracting gives
-<math>\label{IV}
+\begin{eqnarray*}
-f_8(Y)-f_8(Y^\prime)=-\frac{1}{2}[a_+f_6\nabla^-_1+b_+f_7\nabla_2^-]\tag{IV}
+f_8(Y)-f_8(Y^\prime)=-\frac{1}{2}[a_+f_6\nabla^-_1+b_+f_7\nabla_2^-]\tag{IV}\\
-</math>\\
+a[-2a_+f_1-2f_2-b_+f_3-f_6\nabla^+_1]=0\tag{V}\\
-<math>\label{V}
+b[-2b_+f_4-2f_5-a_+f_3-f_7\nabla^+_2]=0\tag{VI}\\
-a[-2a_+f_1-2f_2-b_+f_3-f_6\nabla^+_1]=0\tag{V}
+\end{eqnarray*}
 Adding the two forms gives