% this tex file was generated by the Physics Derivation Graph 
\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage[dvipdfmx,colorlinks=true,pdfkeywords={physics derivation graph}]{hyperref}
\usepackage{graphicx} % for including PNG files
% inference rules as newcommand for use in the body
\newcommand\declareinitialexpression[1]{Eq.~\ref{eq:#1} is an initial equation.}
\newcommand\substituteLHSofexprintoexpr[3]{Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.}
\newcommand\subtractXfrombothsides[3]{Subtract $#1$ from both sides of Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.}
\newcommand\swapLHSwithRHS[2]{Swap LHS of Eq.~\ref{eq:#1} with RHS; yields Eq.~\ref{eq:#2}.}
\newcommand\multiplyexprbyexpr[3]{Multiply Eq.~\ref{eq:#1} by Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.}
\title{Compton's equation for scattering}
\date{\today}
%\author{a84c8294ad9547db4da22820fcaf8c7215485d84d522c45d981703b9995138ba}
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\begin{document}
\maketitle
\begin{abstract}
Generated by the \href{http://allofphysics.com/}{Physics Derivation Graph}.
\end{abstract}

% step ID = 0008668018
\declareinitialexpression{de3166fd245327e41c9db2784e8642cc3edcc854a1d553c6846de5da72284926}
\begin{equation}
\vec{p}_{\rm before} = \vec{p}_{\rm after}
\label{eq:de3166fd245327e41c9db2784e8642cc3edcc854a1d553c6846de5da72284926}
\end{equation}

% step ID = 0003445641
\declareinitialexpression{26d84efa3f2a95e0b9c1aaae4aff941674dcf092e52051c25815691280382daa}
\begin{equation}
\vec{p}_{\rm before} = \vec{p}_{1}
\label{eq:26d84efa3f2a95e0b9c1aaae4aff941674dcf092e52051c25815691280382daa}
\end{equation}

% step ID = 0004733986
\declareinitialexpression{4c72d87389a20ef214250d12e336766389f5f1fec9b8aa7d90cf6996b03cd55a}
\begin{equation}
\vec{p}_{\rm after} = \vec{p}_{2}+\vec{p}_{electron}
\label{eq:4c72d87389a20ef214250d12e336766389f5f1fec9b8aa7d90cf6996b03cd55a}
\end{equation}

% step ID = 0007958085
\substituteLHSofexprintoexpr{de3166fd245327e41c9db2784e8642cc3edcc854a1d553c6846de5da72284926}{26d84efa3f2a95e0b9c1aaae4aff941674dcf092e52051c25815691280382daa}{d8786670096883df28291e72a167ad24db404ac55c905a7729e4cd246115693a}
\begin{equation}
\vec{p}_{\rm after} = \vec{p}_{1}
\label{eq:d8786670096883df28291e72a167ad24db404ac55c905a7729e4cd246115693a}
\end{equation}

% step ID = 0003667395
\substituteLHSofexprintoexpr{4c72d87389a20ef214250d12e336766389f5f1fec9b8aa7d90cf6996b03cd55a}{d8786670096883df28291e72a167ad24db404ac55c905a7729e4cd246115693a}{a8b1ee6557e297c11a881d31d223ff5b4406871fe2796ff370d01827f3065b1b}
\begin{equation}
\vec{p}_{1} = \vec{p}_{2}+\vec{p}_{electron}
\label{eq:a8b1ee6557e297c11a881d31d223ff5b4406871fe2796ff370d01827f3065b1b}
\end{equation}

% step ID = 0007952658
\subtractXfrombothsides{\vec{p}_{2}}{a8b1ee6557e297c11a881d31d223ff5b4406871fe2796ff370d01827f3065b1b}{f984a5f62de461f214ea55454fcdea406f3dcdb2bae1fad580811778522422bb}
\begin{equation}
\vec{p}_{1}-\vec{p}_{2} = \vec{p}_{electron}
\label{eq:f984a5f62de461f214ea55454fcdea406f3dcdb2bae1fad580811778522422bb}
\end{equation}

% step ID = 0003871228
\swapLHSwithRHS{f984a5f62de461f214ea55454fcdea406f3dcdb2bae1fad580811778522422bb}{8b78dabc194ff0ee031afdb028fdf22e1b6cd1f5262c61519cde7cb087989ddf}
\begin{equation}
\vec{p}_{electron} = \vec{p}_{1}-\vec{p}_{2}
\label{eq:8b78dabc194ff0ee031afdb028fdf22e1b6cd1f5262c61519cde7cb087989ddf}
\end{equation}

% step ID = 0004738354
\multiplyexprbyexpr{8b78dabc194ff0ee031afdb028fdf22e1b6cd1f5262c61519cde7cb087989ddf}{8b78dabc194ff0ee031afdb028fdf22e1b6cd1f5262c61519cde7cb087989ddf}{3a1fcd45f9ac1bec90821976600e622c43c2ef56e2eab8b811d7651300246c2a}
\begin{equation}
\vec{p}_{electron}\cdot\vec{p}_{electron} = ( \vec{p}_{1}\cdot\vec{p}_{1})+( \vec{p}_{2}\cdot\vec{p}_{2})-2( \vec{p}_{1}\cdot\vec{p}_{2})
\label{eq:3a1fcd45f9ac1bec90821976600e622c43c2ef56e2eab8b811d7651300246c2a}
\end{equation}
\bibliographystyle{plain}
\bibliography{pdg_derivation_citations.bib}
\end{document}
% EOF