$ \newcommand{\braket}[1]{\langle #1 \rangle}
\newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}}
\newcommand{\ket}[1]{\left\lvert#1 \right.\rangle}
\newcommand{\bra}[1]{\langle\left. #1\right\rvert}
\newcommand{\braket}[1]{\langle #1 \rangle}
\newcommand{\dd}{\text{d}}
\newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}}
\newcommand{\pdv}[2]{\frac{\partial}{\partial #1}}
$
