$$
\newcommand{\vb}{\mathbf}
\newcommand{\wt}{\widetilde}
\newcommand{\mc}{\mathcal}
\newcommand{\bmc}[1]{\boldsymbol{\mathcal{#1}}}
\newcommand{\sup}[1]{^{\text{#1}}}
\newcommand{\pard}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\VMV}[3]{ \Big\langle #1 \Big| #2 \Big| #3 \Big\rangle}
$$