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+% braket.sty Macros for Dirac bra-ket <|> notation and sets {|}
+% Donald Arseneau asnd@triumf.ca Last modified 05-May-2005.
+% This is free, unencumbered, unsupported software.
+%
+% Commands defined are:
+% \bra{ } \ket{ } \braket{ } \set{ } (small versions)
+% \Bra{ } \Ket{ } \Braket{ } \Set{ } (expanding versions)
+%
+% The "small versions" use fixed-size brackets independent of their
+% contents, whereas the "expanding versions" make the brackets and
+% vertical lines expand to envelop their contents (internally using
+% the \left and \right commands). You should use the vertical bar
+% character "|" to input any extra vertical lines. In \Braket these
+% vertical lines will expand to match the arguments, and in \Set the
+% first vertical will expand. E.g.,
+%
+% \Braket{ \phi | \frac{\partial^2}{\partial t^2} | \psi }
+% \Set{ x\in\mathbf{R}^2 | 0<{|x|}<5 }
+%
+% Likewise, you may make an expandable double-bar using either
+% the "\|" command or its local alias "||".
+%
+% NOT defined is "\ketbra" (for projection operators) because I prefer
+% \ket{ } \bra{ }.
+%
+% Because each definition is so small, it makes no sense to have a
+% complicated generic version for many bracket styles. Instead,
+% you can just copy the definitions and change \langle or \rangle,
+% < and > to what you like.
+%
+\def\bra#1{\mathinner{\langle{#1}|}}
+\def\ket#1{\mathinner{|{#1}\rangle}}
+\def\braket#1{\mathinner{\langle{#1}\rangle}}
+\def\Bra#1{\left<#1\right|}
+\def\Ket#1{\left|#1\right>}
+{\catcode`\|=\active
+ \gdef\Braket#1{\begingroup
+ \ifx\SavedDoubleVert\relax
+ \let\SavedDoubleVert\|\let\|\BraDoubleVert
+ \fi
+ \mathcode`\|32768\let|\BraVert
+ \left<{#1}\right>\endgroup}
+}
+\def\BraVert{\@ifnextchar|{\|\@gobble}% turn || into \|
+ {\egroup\,\mid@vertical\,\bgroup}}
+\def\BraDoubleVert{\egroup\,\mid@dblvertical\,\bgroup}
+\let\SavedDoubleVert\relax
+
+% The \mid@vertical is \vrule with ordinary TeX but \middle| in eTeX.
+% We always avoid a \mathchoice in making the inner vertical lines.
+% Note that \right>, prints the same as \right\rangle but is faster.
+%
+% \def\ketbra#1#2{\ket{#1}\bra{#2}}
+% \def\Ketbra#1#2{\left|{#1}\vphantom{#2}\right>\left<{#2}\vphantom{#1}\right|}
+
+% \Set{...|...} Only the first | is treated specially.
+{\catcode`\|=\active
+ \gdef\set#1{\mathinner{\lbrace\,{\mathcode`\|32768\let|\midvert #1}\,\rbrace}}
+ \gdef\Set#1{\left\{
+ \ifx\SavedDoubleVert\relax \let\SavedDoubleVert\|\fi
+ \:{\let\|\SetDoubleVert
+ \mathcode`\|32768\let|\SetVert
+ #1}\:\right\}}
+}
+\def\midvert{\egroup\mid\bgroup}
+\def\SetVert{\@ifnextchar|{\|\@gobble}% turn || into \|
+ {\egroup\;\mid@vertical\;\bgroup}}
+\def\SetDoubleVert{\egroup\;\mid@dblvertical\;\bgroup}
+
+% If the user is using e-TeX with its \middle primitive, use that for
+% verticals instead of \vrule.
+%
+\begingroup
+ \edef\@tempa{\meaning\middle}
+ \edef\@tempb{\string\middle}
+\expandafter \endgroup \ifx\@tempa\@tempb
+ \def\mid@vertical{\middle|}
+ \def\mid@dblvertical{\middle\SavedDoubleVert}
+\else
+ \def\mid@vertical{\mskip1mu\vrule\mskip1mu}
+ \def\mid@dblvertical{\mskip1mu\vrule\mskip2.5mu\vrule\mskip1mu}
+\fi
+
+% May 2005: Double verticals; tweak spacing.