How can the following command be implemented with \NewDocumentCommand?:
\def\bracket<#1|#2>{
\left\langle #1 \right|\left. #2 \right\rangle
}
MWE
\documentclass[]{article}
\def\bracket<#1|#2>{
\left\langle #1 \right|\left. #2 \right\rangle
}
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
Make IMHO not really sense, but if you want:
\documentclass{article}
\makeatletter
\NewDocumentCommand{\bracket}{r<|}{%
\typeout{TRACE1: \detokenize{#1}}%
\@bracket{#1}|%
}
\NewDocumentCommand{\@bracket}{mr|>}{%
\left\langle #1\middle|#2\right\rangle
}
\makeatother
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
or with one macro:
\documentclass{article}
\NewDocumentCommand{\bracket}{e{<}r|>}{%
\left\langle #1\middle|#2\right\rangle
}
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
But IMHO better would be something like:
\documentclass{article}
\ExplSyntaxOn
\NewDocumentCommand{\bracket}{r<>}
{
\seq_set_split:Nnn \l_tmpa_seq { | } { #1 }
\seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl
\left\langle \l_tmpa_tl
\seq_map_inline:Nn \l_tmpa_seq { \middle | ##1 }
\right\rangle
}
\ExplSyntaxOff
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\bracket<\phi>
\bracket<>
\bracket<\phi|\phi|\phi>
\end{equation}
\end{document}
or easier:
\documentclass{article}
\ExplSyntaxOn
\NewDocumentCommand{\bracket}{r<>}
{
\tl_set:Nn \l_tmpa_tl { #1 }
\tl_replace_all:Nnn \l_tmpa_tl { | } { \middle | }
\left\langle \l_tmpa_tl \right\rangle
}
\ExplSyntaxOff
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\bracket<\phi>
\bracket<>
\bracket<\phi|\phi|\phi>
\end{equation}
\end{document}
Both result in:
Trust me: you don't want automatic sizing. Just look at the last two examples.
\documentclass[twocolumn]{article}
\usepackage{amsmath}
\usepackage{mleftright}
\NewDocumentCommand{\bracket}{s O{} >{\SplitArgument{1}{|}}r<>}{%
% #1 = optional * for \left and \right
% #2 = optional size command \big \Big ...
% #3 = the main argument (required to be in <>)
\IfBooleanTF{#1}{% automatic sizing
\mleft\langle\makebracket{\;\middle|\;}#3\mright\rangle
}{% no automatic sizing
\mathopen{#2\langle}\makebracket{\mathrel{#2|}}#3\mathclose{#2\rangle}%
}%
}
\NewDocumentCommand{\makebracket}{mmm}{%
% #1 = middle delimiter
% #2 = before |
% #3 = after | (if present)
#2 \IfValueT{#3}{#1 #3}%
}
\begin{document}
\begin{gather}
\bracket<a> \\
\bracket<a|b> \\
\bracket[\big]<a> \\
\bracket[\big]<a | b> \\
\bracket[\bigg]<\sum_{k=1}^n a_k | x> \\
\bracket*<\sum_{k=1}^n a_k | x>
\end{gather}
\end{document}
Note: twocolumn is just to make a smaller picture.
The optional and required arguments (the last one delimited inside <>) are preprocessed and control is then passed to \makebracket that typesets the inner part.
In general, ltcmd is intended for providing 'regular' LaTeX syntax, although it does allow some more flexible forms. Here, I would read the request as a require delimited argument which is split into two parts: similar to picture mode (..,..) in that sense:
\documentclass{article}
\NewDocumentCommand\bracket{>{\SplitArgument{1}{|}} R<>{|}}
{\bracketaux#1}
\newcommand*\bracketaux[2]{\left\langle #1 \right|\left. #2 \right\rangle}
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
[This is not an answer to the question of how to do it using \NewDocumentCommand from ltcmd/xparse.]
I might probably not bother using ltcmd/xparse at all.
Instead of \def I might probably just use expl3's \cs_new_protected:Npn; this way the command is protected in some expansion-contexts and you get a message in case defining implies overriding a definition already provided.
\documentclass[]{article}
\ExplSyntaxOn
\cs_new_protected:Npn\bracket<#1|#2>{\left\langle#1\middle|#2\right\rangle}
\ExplSyntaxOff
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
I found a way (don't know, if there is a better way):
\documentclass[]{article}
\NewDocumentCommand{\bracket}{e<d|>}{
\left\langle #1 \right|\left. #2 \right\rangle
}
\begin{document}
\begin{equation}
\bracket<\phi|\phi>
\end{equation}
\end{document}
\bracket<\phi^2|\phi> breaks silently. \bracket |\phi> also doesn't yield an error message.
Commented
Mar 10 at 20:44
\NewDocumentCommand\bracket{}{\brackethelp} \def\brackethelp<#1|#2>{\left\langle #1 \right|\left. #2 \right\rangle}qualify?\bracket<\phi|\phi>looks that much clearer than\bracket{\phi}{\phi}? Also, please note that there is a package for braket notation namedbraket, maybe you want to give it a try instead fo reinventing the wheel?\NewDocumentCommand, the whole idea of it is to implement standard argument types, all the more exotic ones are discouraged, better stick to\def, imho, maybe add an\@ifdefinable\racketto ensure the macro doesn't conflict with things. Also, inbraketthe syntax would be something like\braket{\phi|\phi}, not too far off from yours, but way more LaTeXy.\left\langle #1 \right|\left. #2 \right\rangledoes not ensure the < and > have the same size which is rather weird. why not\left\langle #1 \middle| #2 \right\rangle????