New Command acting around selected text

Question

I would like to make a new command that allows me to quickly write the expectation value of an operator. It should put text in between other commands to make the following:

$\langle \psi | text | \psi \rangle$

through using a new command like this:

\newcommand{\expectation}{\langle \psi {text} \psi \rangle}
$\expectation{text}$

What is the correct way of formatting this?

Answer 1

A syntax for a custom macro can be \newcommand{\<macroname>}[<number of arguments>]{<macro code with #1 as first argument, #2 second ...>}.

In your case, the macro can be defined as \newcommand{\expectation}[1]{\langle \psi #1 \psi \rangle}.

More information can be retrieved from wikibooks/latex/macros. You should also have a look at the xparse package which provides enhanced macro definition capabilities.

Answer 2

The mathtools package provides a way to define such commands. The documentation contains a definition for \braket and you can build on this to get an \expectation macro with similar properties, namely that \expectation* rescales automatically, and \expectation, \expectation[\big], \expectation[\Big], \expectation[\bigg], etc., produce specific sizes:

\documentclass{article}

\usepackage{mathtools}

\DeclarePairedDelimiterX{\braket}[3]{\langle}{\rangle}{#1
\,\delimsize\vert\,\mathopen{} #2 \,\delimsize\vert\, \mathopen{}
#3}

\NewDocumentCommand{\expectation}{ s O{} m }{
  \IfBooleanTF {#1}
  { \braket*{\psi}{#3}{\psi} }
  { \braket[#2]{\psi}{#3}{\psi} }
  }

\begin{document}

\( \braket{\psi}{X}{\phi} \) \( \expectation{X} \)

\( \braket{\psi}{A^{2}}{\phi} \) \( \expectation{A^{2}} \)

Manual sizing
\begin{equation*}
  \braket[\bigg]{\psi}{\sum_{i=1}^{n}}{\phi}
  \expectation[\bigg]{\sum_{i=1}^{n} B_{i}}
\end{equation*}
\( \braket[\big]{\psi}{A^{2}}{\phi} \) \( \expectation[\big]{A^{2}} \)

Automatic sizing
\begin{equation*}
  \braket*{\psi}{\sum_{i=1}^{n}}{\phi}
  \expectation*{\sum_{i=1}^{n} B_{i}}
\end{equation*}

\end{document}

Answer 3

It is much better to use the following definition: \newcommand{\expectation}[1]{\left\langle\psi\left\lvert{#1}\right\rvert\psi\right\rangle}. In this way the size of the angular brackets adapts to the size of the argument.