How to make pipe to grow with both sides?

Question

How to make pipe (vertical bar) symbol to grow like in Dirac product notation but without outer angle brackets?

Answer 1

Usually LaTeX is used with e-TeX that provides \middle:

\documentclass{article}
\begin{document}
\[
  \left. a \middle| b \right.
\]
\end{document}

The extra spaces of \left. and \right. would probably would make sense, but they can be reduced by package mleftright:

\documentclass{article}
\usepackage{mleftright}
\begin{document}
\[
  \mleft. a \middle| b \mright.
\]
\end{document}

If the vertical bar is used like a relational symbol, then the spacing is achieved by

\left. a \mathrel{}\middle|\mathrel{} b \right.

e-TeX does not insert space between a math rel atom and the closing delimiter, the left side of \middle, and it does not insert space between the opening delimiter, the right side of \middle, and a math rel atom.

An alternative is

\left. a \nonscript\;\middle|\nonscript\; b \right.

\nonscript suppresses the following space if in \scriptstyle or \scriptscriptstyle, where TeX also would not set space around relational symbols. There are differences to the previous method for punctuation characters (unlikely here), other relational symbols (unlikely probably) and open/close delimiters, e.g.:

\documentclass{article}
\usepackage{mleftright}
\begin{document}
\[
  \mleft.(\mathrel{}\middle|\mathrel{})\mright.
\]
\[
  \mleft.(\nonscript\;\middle|\nonscript\;)\mright.
\]
\end{document}

For a binary operator the space would be \> (medium space) instead of \; (thick space):

\mleft. a \nonscript\;\middle|\nonscript\; b\mright.

The behaviour is a little closer to a binary operator with the following construct:

\left.a \mathbin{}{\nonscript\mkern-\medmuskip}\middle|{\nonscript\mkern-\medmuskip} \mathbin{} b\right.

Either way, it is a good idea to hide the implementation details in a markup macro.

Answer 2

Package braket defines some macros that can be used here.

While it defines only commands that uses angle brackets or braces (for sets), one can easily copy-edit the specification for \Braket to make their own \Pipe.

Advantages over the very similar solution of Heiko Oberdiek is

1. The usage of a macro.
2. You don't need to provide the \middle command (it is used internally) and just use plain | or, for double pipes, || and \|.

Code

\documentclass{article}
\usepackage{braket}
\usepackage{amsmath}
\usepackage{mleftright} % 

% the following lines are borrowed from braket
{\catcode`\|=\active
  \xdef\Pipe{\protect\expandafter\noexpand\csname Pipe \endcsname}
  \expandafter\gdef\csname Pipe \endcsname#1{\begingroup
     \ifx\SavedDoubleVert\relax
       \let\SavedDoubleVert\|\let\|\BraDoubleVert
     \fi
     \mathcode`\|32768\let|\BraVert
     \left.{#1}\right.\endgroup}
}

% with package mleftright:
{\catcode`\|=\active
  \xdef\mPipe{\protect\expandafter\noexpand\csname mPipe \endcsname}
  \expandafter\gdef\csname mPipe \endcsname#1{\begingroup
     \ifx\SavedDoubleVert\relax
       \let\SavedDoubleVert\|\let\|\BraDoubleVert
     \fi
     \mathcode`\|32768\let|\BraVert
     \mleft.{#1}\mright.\endgroup}
}
\begin{document}\noindent
$y  \Pipe{\dfrac{1}{2} | x_2 } z $ \\
$y \mPipe{\dfrac{1}{2} | x_2 } z $ \\
\end{document}

Output

Answer 3

You can preface delimiters with \left and \right in order to have them automatically sized. If you only have one delimiter, you can use . in place of the other one, as in

\left. \frac{1}{2} \right|

So if you know which side of the bar is bigger, you can try something like this:

\left\langle \left. \frac{1}{2} \psi_1 \right| \psi_2 \right\rangle