Braket notation in LaTeX

Question

I am using the braket package to generate bra and ket vectors. However, I could not figure out how to do <0|0> using the package. Is there a command for this?

Answer 1

Use \braket{0|0}:

\documentclass{standalone}

\usepackage{braket}

\begin{document}

$\braket{0|0}$

\end{document}

Answer 2

There is the physics package:

\documentclass{article}
\usepackage{physics}
\begin{document}
  $\bra{\Psi}\ket{\Psi}$ $\expval{A}{\Psi}$
\end{document}

It offers many other goodies for typsetting physics things. Details can be found in the manul (texdoc physics from command prompt/terminal).

Edit by @Gaussler in 2023: Do not use the physics package at all. To quote Henri Menke’s comment below, “[t]he implementation is really horrible and it destroys the spacing all over the place.” To put it differently, physics belongs together with commath in package hell. Use one of the solutions from the other answers instead.

Answer 3

A solution using the mathtools package:

\documentclass{article}

\usepackage{mathtools}
\DeclarePairedDelimiter\bra{\langle}{\rvert}
\DeclarePairedDelimiter\ket{\lvert}{\rangle}
\DeclarePairedDelimiterX\braket[2]{\langle}{\rangle}{#1\,\delimsize\vert\,\mathopen{}#2}

\begin{document}

\begin{align*}
  \bra{a}       &= \bra*{\frac{a}{1}} \\
  \ket{a}       &= \ket*{\frac{a}{1}} \\
  \braket{a}{b} &= \braket*{\frac{a}{1}}{\frac{b}{1}}
\end{align*}

\end{document}

Notice that the starred versions of the macros scale automatically.

Answer 4

You can use the \langle and \rangle commands. For example, to do <0|0>, you would do:

\langle 0 | 0 \rangle

Result:

If you have things which use vertical space (like fractions), you can use \left, \right and \middle to adjust the vertical size of the <, > and | symbols. For example:

\left\langle \frac{1}{2} \middle| 1 \right\rangle

Result:

Answer 5

A complement to the answers above. In case one wants to have a different operators in the left/right and want something in the middle the \expval does no help. An option is to use the \matrixelement in the physics package. This also have the advantage of the proper scaling of the bras & kets for disproportional operators.

\documentclass{article}
\usepackage{physics}
\begin{document}
\begin{equation}
 \mel{n}{A}{m}
\end{equation}
\end{document}