deletions | additions       diff --git a/header.tex b/header.tex  index b754b40..f424265 100644  --- a/header.tex  +++ b/header.tex 
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\newcommand{\bra}[1] \newcommand{\ket}[1]  {| {#1} \rangle} \newcommand{\ket}[1] \newcommand{\bra}[1]  {\langle {#1} |} \newcommand{\braket}[2] {\langle {#1} | {#2} \rangle}  \newcommand{\ketbra}[2] {\ket{#1}\bra{#2}} \newcommand{\braoket}[3]{\langle {#1} | {#2} | {#3} \rangle}