Finish 3.8.2-3.8.5 and small fixes in chap. 2, 3, 6 (#29)

* small fixes in chap6 * small fixes in Chap 2 and 3 * 3.8.2 finished * 3.8.3-5 finished
NominHanggai · Jul 5, 2023 · cdc5260 · cdc5260
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diff --git a/Chaps/Chap2.tex b/Chaps/Chap2.tex
@@ -2075,13 +2075,13 @@ \subsection{矩阵元规则的推导}
 都无法使积分不为0(因为自旋轨道相互正交). 
 因此
 \begin{equation}
-\braket{K|\mathcal{O}_1|K} = 0 \qquad \textit{情形3}
+\braket{K|\mathcal{O}_1|L} = 0 \qquad \textit{情形3}
 \end{equation}
 
 现在来考察双电子算符, 
 一般的双电子算符矩阵元有如下形式:
 \begin{equation}
-\braket{K|\mathcal{O}_2|K} = \braket{K|r^{-1}_{12}+r^{-1}_{13}+r^{-1}_{14}+\cdots+r^{-1}_{23}+r^{-1}_{24}+\cdots+r^{-1}_{N-1,N}}
+\braket{K|\mathcal{O}_2|L} = \braket{K|r^{-1}_{12}+r^{-1}_{13}+r^{-1}_{14}+\cdots+r^{-1}_{23}+r^{-1}_{24}+\cdots+r^{-1}_{N-1,N}|L}
 \end{equation}
 其中的加和遍及所有电子对. 
 由于行列式并不区分全同电子, 
@@ -3317,6 +3317,7 @@ \subsection{自旋算符}
 37). 
 写出来就是
 \begin{align}
+\label{2.254}
 \ts_z\ket{\chi_i\chi_j\cdots\chi_k} = \frac{1}{2}(N^\alpha - N_\beta)\ket{\chi_i\chi_j\cdots\chi_k} = M_S\ket{\chi_i\chi_j\cdots\chi_k}
 \end{align}
 式中$N^\alpha$是具有$\alpha$自旋的轨道数目,