Would you be averse to writing $\langle x\mid y\rangle$ instead of $\left< x \middle| y\right>$? — Michael Hardy 6 hours ago

@MichaelHardy I do kinda like the extra spacing from \mid, though unfortunately it doesn't scale (at least not with \middle\mid), so at the moment I wouldn't bother with it. I guess if we cared for the space, it could be \newcommand{\bk}[2]{\left< #1 \hspace{5px} \middle| \hspace{5px} #2 \right>} instead. Or, maybe a bit less than 5px, since it looks a bit much. — Nat 6 hours ago