如果有意义的话，我希望能够清晰地遵循从方程 1 到方程 2（a 或 b）再到方程 3a（a 或 b）再到方程 4aa（a 或 b）等的推导过程。我目前正在使用内置子方程环境来尝试执行此操作，但它只有默认计数器 3，这对我来说还不够，因为方程 3 在我的长推导中不断重复。
GPT 建议我创建一个自定义环境，其中的无限计数器在函数中镜像 subeqn，但对我来说不起作用。我想知道子方程环境是否真的是我想要的，或者是否有更好的方法，我不知道我应该考虑。
\usepackage{physics}
\usepackage{breqn}
\title{FCI Questions}
\author{Patryk Kozlowski}
\date{\today} %% Change "\today" by another date manually
\begin{document}
\maketitle
\section{0 differences between two determines}
\begin{equation}
\mel{\Psi }{V}{\Psi }
=v^{\alpha\beta\gamma\delta}\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{1}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{equation}
\begin{subequations}
\begin{align}
=\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }\delta _{\delta \kappa _{1}}
\left(\prod_{\kappa^{\prime}=\left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }a^{\dag}_{\kappa _{1}}a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta \kappa _{1}}\delta _{\gamma \kappa _{2}}
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta_{\kappa _{1}}}a^{\dag}_{\kappa _{2}}a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\begin{subequations}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{'}a^{\dag}_{\beta }\delta _{\gamma \kappa _{1}}a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a^{\dag}_{\kappa _{1}}a_{\gamma }a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
a_{\kappa _{2}}a_{\kappa _{1}}a^{\dag}_{\kappa _{2}}a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta \kappa _{1}}a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\begin{subequations}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
\delta _{\gamma \kappa _{1}}a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta \kappa _{2}}
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
\delta _{\gamma \kappa _{1}}a^{\dag}_{\alpha }a^{\dag}_{\beta }a^{\dag}_{\kappa _{2}}a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{subequations}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}\delta _{\alpha \kappa _{1}}a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}a^{\dag}_{\alpha }a_{\kappa _{1}}a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{align}
-\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma\kappa _{1}}\delta _{\delta \kappa _{2}}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\gamma \kappa _{1}}a_{\kappa _{1}}a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\delta \kappa _{1}}\delta _{\alpha \kappa _{1}}\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{subequations}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}a^{\dag}_{\alpha }
\delta _{\beta \kappa _{1}}
a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}a^{\dag}_{\alpha }a_{\kappa _{1}}a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{align}
-\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma\kappa _{1}}\delta _{\delta \kappa _{2}}
\end{align}
\begin{subequations}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\gamma \kappa _{1}}\delta _{\alpha \kappa _{1}}a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\gamma \kappa _{1}}a^{\dag}_{\alpha }a_{\kappa _{1}}a^{\dag}_{\beta }a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\alpha \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
-\delta _{\beta \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{
_{2}
}H_{0}a_{
_{2}
}a_{1}
a_{
\kappa _{2}
}
}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
+\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}a^{\dag}_{\alpha }\delta _{\beta \kappa _{1}}a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
-\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
\delta _{\delta \kappa _{1}}a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\kappa _{1}}a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{align}
-\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{1}}\delta _{\delta \kappa _{2}}
\end{align}
\begin{subequations}
\begin{align}
-\delta _{\gamma \kappa _{1}}\delta _{\alpha \kappa _{1}}\mel{\Psi}{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\gamma \kappa _{1}}\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{3}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }\delta _{\beta \kappa _{1}}a_{\gamma }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\begin{align}
-0
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\alpha \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
-\delta _{\beta \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{
_{2}
}H_{0}a_{
_{2}
}a_{1}
a_{
\kappa _{2}
}
}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\beta \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{align}
-0
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{align}
-\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{1}}\delta _{\delta \kappa _{2}}
\end{align}
\begin{subequations}
\begin{align}
-\delta _{\gamma \kappa _{1}}\delta _{\alpha \kappa _{1}}\mel{\Psi}{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{subequations}
\begin{align}
+\delta _{\gamma \kappa _{1}}\delta _{\beta \kappa _{1}}\mel{\Psi}{a^{\dag}_{\kappa _{1}a^{\dag}_{\kappa _{2}}}H_{0} a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{align}
-0
\end{align}
\end{subequations}
\end{subequations}
\end{subequations}
\begin{subequations}
\begin{subequations}
\begin{align}
=\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{2}}\delta _{\delta \kappa _{1}}
\end{align}
\begin{align}
-\delta _{\alpha \kappa _{1}}\delta _{\beta \kappa _{2}}\delta _{\gamma \kappa _{1}}\delta _{\delta \kappa _{2}}
\end{align}
\end{subequations}
\begin{subequations}
\begin{align}
+\delta _{\alpha \kappa _{1}}\delta _{\delta \kappa _{1}}\mel{\Psi }{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{align}
+\delta _{\gamma \kappa _{1}}\delta _{\beta \kappa _{1}}\mel{\Psi}{a^{\dag}_{\kappa _{1}a^{\dag}_{\kappa _{2}}}H_{0} a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\begin{align}
-\delta _{\gamma \kappa _{1}}\delta _{\alpha \kappa _{1}}\mel{\Psi}{a^{\dag}_{\kappa _{1}}a^{\dag}_{\kappa _{2}}H_{0}a_{\kappa _{2}}a_{\kappa _{1}}}{\Psi }
\end{align}
\end{subequations}
\end{subequations}
\text{adding the integrals back in.}
\begin{subequations}
\begin{subequations}
\begin{align}
=v^{\kappa _{1}\kappa _{2}\kappa _{2}\kappa _{1}}
\end{align}
\begin{align}
-v^{\kappa _{1}\kappa _{2}\kappa _{1}\kappa _{2}}
\end{align}
\end{subequations}
\begin{subequations}
\begin{align}
+v^{\kappa _{1}\beta \gamma \kappa _{1}}
\end{align}
\begin{align}
+v^{\alpha \kappa _{1}\kappa _{1}\delta }
\end{align}
\begin{align}
-v^{\kappa _{1}\beta \kappa _{1}\delta }
\end{align}
\end{subequations}
\end{subequations}
\text{equation 3 part b similar to the Condon roles. not sure were to go with this, or with part a}
\section{math_drafts.pdf}
I'm confused about the steps you took to get from
\begin{equation}
\sum_{\kappa }h^{\kappa \kappa }
\end{equation}
\begin{equation}
\sum_{\kappa } h^{(\kappa )(\kappa )}\delta _{[\kappa ],[\kappa ]}
\end{equation}
\end{document}
答案1
一种可能的方法是使用align并保持简单。取冗长示例中的前几行公式，然后：
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{physics}
\begin{document}
\section{differences between two determines}
\begin{align}
\mel{\Psi }{V}{\Psi } &= v^{\alpha\beta\gamma\delta}\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{1}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0} \\
&= \bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right) a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }\delta _{\delta \kappa _{1}} \left(\prod_{\kappa^{\prime}= \left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0} \\
& \hspace{5mm} -\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }a^{\dag}_{\kappa _{1}}a_{\delta }
\left(\prod_{\kappa^{\prime}=\left(\kappa_{2}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0} \\
&= \bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta \kappa _{1}}\delta _{\gamma \kappa _{2}}
\left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0} \\
& \hspace{5mm} - \bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right)
a^{\dag}_{\alpha }a^{\dag}_{\beta }\delta _{\delta_{\kappa _{1}}}a^{\dag}_{\kappa _{2}}a_{\gamma } \left(\prod_{\kappa^{\prime}=\left(\kappa_{3}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}
\end{align}
\end{document}
需要注意的是，等号是对齐的，没有等号的行稍微偏移了一点。在这个例子中，方程编号只是计算方程的数量。输出为：
附注：如果这只是为了学习，那么保持简单的格式往往利大于弊。
有多种方法可以制作或使用1.xx第一部分形式的方程计数器、2.xx第二部分形式的方程计数器等等。
答案2
正如@Leucippus 所做的那样他们的答案，我建议您放弃这种subequations方法，采用单一、多页align环境。我还将用 -sized 括号替换所有高括号（大小通过\left(和\right)）\bigg，以使材料的外观更加平衡。
您会发现，在每个方程组的开头插入彩色点或其他视觉标记可以更轻松地追踪推导。
\documentclass{article}
\usepackage{physics,breqn}
\begin{document}
\section{0 differences between two determines}
\allowdisplaybreaks % allow page breaks in long 'align' env.
\begin{align} % use a single 'align' env.
\mel{\Psi}{V}{\Psi}
&=v^{\alpha\beta\gamma\delta}
\bra{0}
\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha} a^{\dag}_{\beta} a_{\gamma} a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_1\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)
\ket{0}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&=\bra{0}
\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}a^{\dag}_{\beta}a_{\gamma}\delta_{\delta\kappa_1}
\biggl(\prod_{\,\kappa'=(\kappa_2\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}a^{\dag}_{\beta}a_{\gamma}a^{\dag}_{\kappa_1}a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_2\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}a^{\dag}_{\beta}\delta_{\delta\kappa_1}\delta_{\gamma \kappa_2}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}a^{\dag}_{\beta}\delta_{\delta_{\kappa_1}}a^{\dag}_{\kappa_2}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{'}a^{\dag}_{\beta}\delta_{\gamma \kappa_1}a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_2\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}a^{\dag}_{\beta}a^{\dag}_{\kappa_1}a_{\gamma}a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_2\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta \kappa_2}\delta_{\gamma \kappa_2}\delta_{\delta\kappa_1}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
a_{\kappa_2}a_{\kappa_1}a^{\dag}_{\kappa_2}a^{\dag}_{\alpha}a^{\dag}_{\beta}
\delta_{\delta\kappa_1}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\gamma \kappa_1}a^{\dag}_{\alpha}a^{\dag}_{\beta}\delta_{\delta\kappa_2}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_1)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\gamma \kappa_1}a^{\dag}_{\alpha}a^{\dag}_{\beta}a^{\dag}_{\kappa_2}a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta \kappa_2}\delta_{\gamma \kappa_2}\delta_{\delta\kappa_1}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}\delta_{\alpha \kappa_1}a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}a^{\dag}_{\alpha}a_{\kappa_1}a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\alpha \kappa_1}\delta_{\beta \kappa_2}\delta_{\gamma\kappa_1}\delta_{\delta\kappa_2}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\gamma \kappa_1}a_{\kappa_1}a^{\dag}_{\alpha}a^{\dag}_{\beta}a_{\delta}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta \kappa_2}\delta_{\gamma \kappa_2}\delta_{\delta\kappa_1}
\\*
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\delta\kappa_1}\delta_{\alpha \kappa_1}\bra{0}
\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}a^{\dag}_{\alpha}\delta_{\beta \kappa_1}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}a^{\dag}_{\alpha}a_{\kappa_1}a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\alpha \kappa_1}\delta_{\beta \kappa_2}\delta_{\gamma\kappa_1}\delta_{\delta\kappa_2}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\gamma\kappa_1}\delta_{\alpha \kappa_1}a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\gamma\kappa_1}a^{\dag}_{\alpha}a_{\kappa_1}a^{\dag}_{\beta}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_2}\delta_{\delta\kappa_1}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\alpha \kappa_1}\delta_{\delta\kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\beta\kappa_1}\delta_{\delta\kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{
_2
}H_0a_{
_2
}a_1
a_{
\kappa_2
}
}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}a^{\dag}_{\alpha}\delta_{\beta\kappa_1}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
&\quad-\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
\delta_{\delta\kappa_1}a^{\dag}_{\alpha} a^{\dag}_{\beta}a_{\kappa_1}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_3\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{align}
&\quad-\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_1}\delta_{\delta\kappa_2}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\gamma\kappa_1}\delta_{\alpha \kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\gamma\kappa_1}\bra{0}\biggl(\prod_{\,\kappa=(\kappa_n\dots\kappa_3)}\mkern-10mu a_{\kappa}\biggr)
a^{\dag}_{\alpha}\delta_{\beta\kappa_1}a_{\gamma}
\biggl(\prod_{\,\kappa'=(\kappa_{}\dots\kappa_n)}\mkern-10mu a^{\dag}_{\kappa'}\biggr)\ket{0}
\\
%\end{align}
%\begin{align}
-0
%\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_2}\delta_{\delta\kappa_1}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\alpha \kappa_1}\delta_{\delta\kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\beta\kappa_1}\delta_{\delta\kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{
_2
}H_0a_{
_2
}a_1
a_{
\kappa_2
}
}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\beta\kappa_1}\delta_{\delta\kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
-0
%\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_1}\delta_{\delta\kappa_2}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad-\delta_{\gamma\kappa_1}\delta_{\alpha \kappa_1}\mel{\Psi}{a^{\dag}_{\kappa_1}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\gamma\kappa_1}\delta_{\beta\kappa_1}
\mel{\Psi}{a^{\dag}_{\kappa_1a^{\dag}_{\kappa_2}}H_0 a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
-0
%\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_2}\delta_{\delta\kappa_1}
\\
%\end{align}
%\begin{align}
&\quad-\delta_{\alpha \kappa_1}\delta_{\beta\kappa_2}\delta_{\gamma\kappa_1}\delta_{\delta\kappa_2}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad+\delta_{\alpha \kappa_1}\delta_{\delta\kappa_1}
\mel{\Psi}{a^{\dag}_{\kappa_1}a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
&\quad+\delta_{\gamma\kappa_1}\delta_{\beta\kappa_1}
\mel{\Psi}{a^{\dag}_{\kappa_1a^{\dag}_{\kappa_2}}H_0 a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
&\quad-\delta_{\gamma\kappa_1}\delta_{\alpha \kappa_1}
\mel{\Psi}{a^{\dag}_{\kappa_1}a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
\intertext{adding the integrals back in.}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=v^{\kappa_1\kappa_2\kappa_2\kappa_1}
\\
%\end{align}
%\begin{align}
&\quad-v^{\kappa_1\kappa_2\kappa_1\kappa_2}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
&\quad+v^{\kappa_1\beta \gamma \kappa_1}
\\
%\end{align}
%\begin{align}
&\quad+v^{\alpha \kappa_1\kappa_1\delta }
\\
%\end{align}
%\begin{align}
&\quad-v^{\kappa_1\beta \kappa_1\delta }
%\end{align}
%\end{subequations}
%\end{subequations}
\end{align}
Equation 3 part b similar to the Condon roles. not sure were to go with this, or with part a.
\section{math\_drafts.pdf}
I'm confused about the steps you took to get from
\begin{gather}
\sum_{\kappa }h^{\kappa \kappa } \\
\sum_{\kappa } h^{(\kappa )(\kappa )}\delta_{[\kappa ],[\kappa ]}
\end{gather}
\end{document}
答案3
这不是一个解决方案，但展示了如何重现子方程编号。
请注意，amsmath 使用计数器parentequation来存储旧的方程数，然后更改\theequation为生成子方程数。这样，它们就可以在环境中使用标准方程subequations。因为\tag创建计数器更容易subequation。不过，也许不是。
\documentclass{article}
\usepackage{amsmath}
\newcounter{subequation}[equation]
\renewcommand{\thesubequation}{\theequation\alph{subequation}}
\begin{document}
\begin{align}
x &= a \\
&= b+c \tag{\stepcounter{subequation}\thesubequation}
\end{align}
%
\begin{subequations}
\begin{align}
x &= a \tag{\theparentequation} \\
&= b+c
\end{align}
\end{subequations}
\end{document}