\newcommand{\bra}[1]{{\left< #1 \right|}}
\newcommand{\ket}[1]{{\left| #1 \right>}}
\newcommand{\braket}[2]{{\left\langle #1\vphantom{#2}\right.\left|\vphantom{#1}#2\right\rangle}}
\newcommand{\dirac}[3]{{\left\langle #1\vphantom{#2}\vphantom{#3}\right| #2 \left|\vphantom{#1}\vphantom{#2}#3\right\rangle}}

\newcommand{\hilbert}{\mathcal{H}}
\newcommand{\one}{\mathbbm{1}}

\newcommand{\probb}[2]{\text{prob}\left[ #1\vphantom{#2} \right. \left| \vphantom{#1}#2 \right]}
\newcommand{\prob}[1]{\text{prob}\left[ #1 \right]}
\newcommand{\diffPs}[1]{\partial_{#1}}