$\newcommand{\vect}[1]{\mathbf{#1}}
\newcommand{\uvect}[1]{\hat{#1}}
\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\norm}[1]{\lVert#1\rVert}
\newcommand{\I}{\mathrm{i}}
\newcommand{\ket}[1]{\left|#1\right\rangle}
\newcommand{\bra}[1]{\left\langle#1\right|}
\newcommand{\braket}[1]{\langle#1\rangle}
\newcommand{\op}[1]{\mathbf{#1}}
\newcommand{\mat}[1]{\mathbf{#1}}
\newcommand{\d}{\mathrm{d}}
\newcommand{\pdiff}[3][]{\frac{\partial^{#1} #2}{\partial {#3}^{#1}}}
\newcommand{\diff}[3][]{\frac{\d^{#1} #2}{\d {#3}^{#1}}}
\newcommand{\ddiff}[3][]{\frac{\delta^{#1} #2}{\delta {#3}^{#1}}}
\DeclareMathOperator{\erf}{erf}
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator{\order}{O}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sech}{sech}
$