$
\newcommand{\I}{\mathrm{i}}
\newcommand{\E}{\mathrm{e}}
\renewcommand{\vec}[1]{\boldsymbol{\mathbf{#1}}}
\newcommand{\mat}[1]{\boldsymbol{\mathbf{#1}}}
\newcommand{\ten}[1]{\boldsymbol{\mathbf{#1}}}
\newcommand{\Nabla}{\vec\nabla}
\renewcommand{\Tr}{^{\mathrm{T}}}
\newcommand{\uvec}[1]{\hat{\boldsymbol{\mathbf{#1}}}}
\renewcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}
\newcommand{\ali}[1]{\begin{aligned}#1\end{aligned}}
\newcommand{\leftgroup}[1]{\left\{\begin{aligned}#1\end{aligned}\right.}
\newcommand{\vmat}[1]{\begin{vmatrix}#1\end{vmatrix}}
\newcommand{\Cj}{^*}
\newcommand{\Her}{^\dagger}
\newcommand{\Q}[1]{\hat #1}
\newcommand{\sinc}{\mathop{\mathrm{sinc}}}
\newcommand{\Si}[1]{\,\mathrm{#1}}
\newcommand{\les}{\leqslant}
\newcommand{\ges}{\geqslant}
\newcommand{\qty}[1]{\left\{{#1}\right\}}
\newcommand{\qtyRound}[1]{\left({#1}\right)}
\newcommand{\qtySquare}[1]{\left[{#1}\right]}
\newcommand{\abs}[1]{\left\lvert{#1}\right\rvert}
\newcommand{\eval}[1]{\left.{#1}\right\rvert}
\newcommand{\comm}[2]{\left[{#1},{#2}\right]}
\newcommand{\commStar}[2]{[{#1},{#2}]}
\newcommand{\pb}[2]{\left\{{#1},{#2}\right\}}
\newcommand{\pbStar}[2]{\{{#1},{#2}\}}
\newcommand{\vdot}{\boldsymbol\cdot}
\newcommand{\cross}{\boldsymbol\times}
\newcommand{\Nabla}{\vec\nabla}
\newcommand{\grad}{\boldsymbol\nabla}
\newcommand{\div}{\vec\nabla\boldsymbol\cdot}
\newcommand{\curl}{\vec\nabla\boldsymbol\times}
\newcommand{\laplacian}{\nabla^2}
\newcommand{\sinRound}[2][{}]{\sin^{#1}\left(#2\right)}
\newcommand{\cosRound}[2][{}]{\cos^{#1}\left(#2\right)}
\newcommand{\tanRound}[2][{}]{\tan^{#1}\left(#2\right)}
\newcommand{\cscRound}[2][{}]{\csc^{#1}\left(#2\right)}
\newcommand{\secRound}[2][{}]{\sec^{#1}\left(#2\right)}
\newcommand{\cotRound}[2][{}]{\cot^{#1}\left(#2\right)}
\newcommand{\sinhRound}[2][{}]{\sinh^{#1}\left(#2\right)}
\newcommand{\coshRound}[2][{}]{\cosh^{#1}\left(#2\right)}
\newcommand{\tanhRound}[2][{}]{\tanh^{#1}\left(#2\right)}
\newcommand{\arcsinRound}[2][{}]{\arcsin^{#1}\left(#2\right)}
\newcommand{\arccosRound}[2][{}]{\arccos^{#1}\left(#2\right)}
\newcommand{\arctanRound}[2][{}]{\arctan^{#1}\left(#2\right)}
\newcommand{\expRound}[1]{\exp\left(#1\right)}
\newcommand{\logRound}[2][{}]{\log^{#1}\left(#2\right)}
\newcommand{\lnRound}[2][{}]{\ln^{#1}\left(#2\right)}
\renewcommand{\Re}{\mathrm{Re}}
\renewcommand{\Im}{\mathrm{Im}}
\newcommand{\dd}[1][]{\,\mathrm{d}^{#1}}
\newcommand{\dv}[2][{}]{\frac{\mathrm{d}^{#1}}{\mathrm{d}{#2}^{#1}}}
\newcommand{\dvStar}[2][{}]{\mathrm{d}^{#1}/\mathrm{d}{#2}^{#1}}
\newcommand{\dvTwo}[3][{}]{\frac{\mathrm{d}^{#1}{#2}}{\mathrm{d}{#3}^{#1}}}
\newcommand{\dvStarTwo}[3][{}]{\mathrm{d}^{#1}{#2}/\mathrm{d}{#3}^{#1}}
\newcommand{\pdv}[2][{}]{\frac{\partial^{#1}}{\partial{#2}^{#1}}}
\newcommand{\pdvStar}[2][{}]{\partial^{#1}/\partial{#2}^{#1}}
\newcommand{\pdvTwo}[3][{}]{\frac{\partial^{#1}{#2}}{\partial{#3}^{#1}}}
\newcommand{\pdvStarTwo}[3][{}]{\partial^{#1}{#2}/\partial{#3}^{#1}}
\newcommand{\pdvThree}[3]{\frac{\partial^2{#1}}{\partial{#2}\partial{#3}}}
\newcommand{\pdvStarThree}[3]{\partial^2{#1}/\partial{#2}\partial{#3}}
\newcommand{\bra}[1]{\left\langle{#1}\right\rvert}
\newcommand{\braStar}[1]{\langle{#1}\rvert}
\newcommand{\ket}[1]{\left\lvert{#1}\right\rangle}
\newcommand{\ketStar}[1]{\lvert{#1}\rangle}
\newcommand{\braket}[2]{\left\langle{#1}\middle|{#2}\right\rangle}
\newcommand{\braketStar}[2]{\langle{#1}|{#2}\rangle}
\newcommand{\ev}[1]{\left\langle{#1}\right\rangle}
\newcommand{\evStar}[1]{\langle{#1}\rangle}
\newcommand{\evTwo}[2]{\left\langle{#2}\middle|{#1}\middle|{#2}\right\rangle}
\newcommand{\evStarTwo}[2]{\langle{#2}|{#1}|{#2}\rangle}
\newcommand{\mel}[3]{\left\langle{#1}\middle|{#2}\middle|{#3}\right\rangle}
\newcommand{\melStar}[3]{\langle{#1}|{#2}|{#3}\rangle}
$
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