8000 fix: correct ket{a} to ket{alpha} in Sec 1.1.6 by renh · Pull Request #79 · nominhanggai/szaboqc · GitHub
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12 changes: 6 additions & 6 deletions Chaps/Chap1.tex
58D6
Original file line number Diff line number Diff line change
Expand Up @@ -876,15 +876,15 @@ \subsection{基组变换}

\subsection{本征值问题}
\label{sec:1.1.6}
算符$\op{O}$作用在一个矢量$\ket{a}$上,
会得到一个新的矢量$\op{O}\ket{a}$。
算符$\op{O}$作用在一个矢量$\ket{\alpha}$上,
会得到一个新的矢量$\op{O}\ket{\alpha}$。
通常情况下,这个新的矢量与原矢量不同。
如果$\op{O}\ket{a}$与$\ket{a}$只差一个常数,即:
如果$\op{O}\ket{\alpha}$与$\ket{\alpha}$只差一个常数,即:
\begin{equation}
\op{O}\ket{a} = \omega_{\alpha}\ket{a}
\op{O}\ket{\alpha} = \omega_{\alpha}\ket{\alpha}
\label{eq:1.72}
\end{equation}
这时,我们可以称$\ket{a}$为算符$\op{O}$关于\emph{本征值} $\omega_{\alpha}$ 的\emph{本征矢量}。将本征矢归一化并不失普遍性:
这时,我们可以称$\ket{\alpha}$为算符$\op{O}$关于\emph{本征值} $\omega_{\alpha}$ 的\emph{本征矢量}。将本征矢归一化并不失普遍性:
\begin{equation}
\olp{\alpha}{\alpha} = 1
\label{eq:1.73}
Expand All @@ -896,7 +896,7 @@ \subsection{本征值问题}
\Mele{\alpha}{O}{\alpha} = \left\langle\alpha\middle\vert\op{O}^\dagger\middle\vert\alpha\right\rangle = {\Mele{\alpha}{O}{\alpha}}^\ast
\label{eq:1.74}
\end{equation}
在\autoref{eq:1.72}两边左乘$\bra{a}$,并带入\autoref{eq:1.74},我们得到:
在\autoref{eq:1.72}两边左乘$\bra{\alpha}$,并带入\autoref{eq:1.74},我们得到:
\begin{equation}
\omega_\alpha = \omega_\alpha^\ast
\label{eq:1.75}
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