# Nesting multiple equations

I want to be able to follow a derivation cleanly from eqn 1 to eqn 2(a or b) to eqn 3a(a or b) to eqn 4aa(a or b), etc. if it makes sense. I am currently using the built-in sub-equation environment to try to do this, but it only has a default counter of 3 and that is not enough for me, as eqn 3 keeps getting Repeated in my long derivation.

GPT suggested that I make a custom env with an unlimited counter that mirrors subeqn in function, but it hasn’t been working for me. I’m wondering if the sub-equation environment is really what I’m looking for, or if there is a better way that I don’t know of that I should be considering.

\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}
$$\mel{\Psi }{V}{\Psi } =v^{\alpha\beta\gamma\delta}\bra{0}\left(\prod_{\kappa=\left(\kappa_{n}\dots\kappa_{1}\right)}a_{\kappa}\right) a^{\dag}_{\alpha }a^{\dag}_{\beta }a_{\gamma }a_{\delta } \left(\prod_{\kappa^{\prime}=\left(\kappa_{1}\dots\kappa_{n}\right)}a^{\dag}_{\kappa^{\prime}}\right)\ket{0}$$
\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}
\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
$$\sum_{\kappa }h^{\kappa \kappa }$$
$$\sum_{\kappa } h^{(\kappa )(\kappa )}\delta _{[\kappa ],[\kappa ]}$$
\end{document}


One possible way is to use align and keep it simple. Taking the first few lines of formulas presented in the lengthy example then:

\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}


It should be noted that the equal signs are aligned and the lines without equal signs are slightly offset. The equation numbering, in this example, just counts the number of equations. The output is:

As a side note: If this is just for study then keeping the format in a simple format may often do more good than bad.

There are various ways to make, or use, equation counters that are of the form 1.xx for section one and 2.xx for section two and so on.

• This is just for personal study, as you deduced, so yes. I have a fine motor impairment, so I am using talon voice to dictate into LaTeX workshop in VSCode. I only mention this because I amusing heavily folding to organize my thoughts, so in that way using nest envs like sub equation is you useful to me, as opposed to just having one align environment with a bunch of &s. can you think of away that it would be possible to nest my equations Still making use of folding? Maybe this would require making heavier use of equation counters? Apr 17 at 21:47
• nevermind, I see that there was an answer that involves equation counters below. Apr 17 at 21:49

As @Leucippus does in their answer, I suggest you drop the subequations approach and employ a single, multi-page align environment. I would also replace all tall parentheses (sized via \left( and \right)) with \bigg-sized parentheses, for a more balanced appearance of the material.

You find it easier to track the derivations by inserting colored dots or other visual markers at the start of each equation group.

\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}
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}
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}
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}
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}
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}
\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}
\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}
\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}
\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}
\\
%\end{align}
%\begin{align}
\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}
\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}
\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}
\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}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
\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}
\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}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
a^{\dag}_{
_2
}H_0a_{
_2
}a_1
a_{
\kappa_2
}
}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
\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}
\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}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
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}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
a^{\dag}_{
_2
}H_0a_{
_2
}a_1
a_{
\kappa_2
}
}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
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}
a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{subequations}
%\begin{align}
\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}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
\mel{\Psi}{a^{\dag}_{\kappa_1}a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
\mel{\Psi}{a^{\dag}_{\kappa_1a^{\dag}_{\kappa_2}}H_0  a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\begin{align}
\mel{\Psi}{a^{\dag}_{\kappa_1}a^{\dag}_{\kappa_2}H_0a_{\kappa_2}a_{\kappa_1}}{\Psi}
\\
%\end{align}
%\end{subequations}
%\end{subequations}
%\begin{subequations}
%\begin{subequations}
%\begin{align}
&=v^{\kappa_1\kappa_2\kappa_2\kappa_1}
\\
%\end{align}
%\begin{align}
\\
%\end{align}
%\end{subequations}
%\begin{subequations}
%\begin{align}
\\
%\end{align}
%\begin{align}
\\
%\end{align}
%\begin{align}
%\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}

• You can retain the subequation numbering using \tag etc. See my partial asnwer below. Apr 17 at 15:43

Not a solution, but showing how to reproduce subequation numbering.

Note that amsmath uses the counter parentequation to store the old equaton number then changes \theequation to produce subequation numbers. That way they can use normal equations inside the subequations environment. For \tag it is easier just to create a subequation counter. Then again, maybe not.

\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}