# How to denote ket notation in LaTeX?

Ket notation is like a kind of bracket, one side of which is bound by single bar and the other side by a right angle bracket.

\documentclass{article}
\begin{document}
$$| a \rangle$$
$$\vert \phi \rangle$$
$$\vert \hat{A} \rangle$$
\end{document}

Output :  Instead of typing such a large syntax, you can define a new command. Latex has multiple methods for defining new commands. However, in this case, the best practice is to use the mathtools package.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\ket{\lvert}{\rangle}
\begin{document}
$$\ket{\psi}$$
$$\hat{p}\ket{p}$$
$$U\ket{a_j}=\ket{Ua_i}$$
$$\ket{1},\ket{2},\ldots,\ket{k}$$
\end{document}

Output :  If you use the star * symbol with to this new command. The size of ket symbol will be adjustable with the argument.

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\ket{\lvert}{\rangle}
\begin{document}
$$\ket*{\Omega }$$
$$\ket*{\Omega^\dagger}$$
$$\ket*{\frac{\Omega^\dagger}{k}}$$
% Passing the Big Command as an optional argument
$$\ket[\big]{\psi} \ket[\Big]{\frac{\psi}{k}}$$
$$\ket[\bigg]{\frac{\psi_i}{n}} \ket[\Bigg]{\frac{\psi_i}{n_k}}$$
\end{document}

Output :  ## Use braket package for ket notation

This package contains two commands \ket and \Ket. In the case of ket command, size will be fixed. For example

\documentclass{article}
\usepackage{braket}
\begin{document}
$$\ket{\psi} = \sum_j \sigma_j\ket{\psi_j}$$
$$\ket{\phi} = A\ket{\psi_i}$$
$$\ket{\frac{\psi_i}{k}}$$
\end{document}

Output :  And it would be best practice to use the \Ket command because the size of the notation and argument will match dynamically.

\documentclass{article}
\usepackage{braket}
\begin{document}
$$\Ket{\frac{m}{k}} = v\Ket{\frac{n}{k}}$$
$$\Ket{\frac{\psi_i}{k}}$$
\end{document}

Output :  \Ket and \ket are considered two separate commands because of latex is case sensitive

## Use physics package in LaTeX

The same command is defined in the physics package as in the bracket package. For example

\documentclass{article}
\usepackage{physics}
\begin{document}
$$v \to \ket{v}$$
$$\ket{v_i} = \sum_{i}\ket{i}\alpha_i$$
$$\ket{v} = \alpha_1\ket{a_1} + \alpha_2\ket{a_2}$$
\end{document}

Output :  Adding a star to the \ket command will make the shape of the notation is constant.

\documentclass{article}
\usepackage{physics}
\begin{document}
$$\ket*{v}$$
$$\ket*{\hat{A}_i}$$
$$\ket*{\frac{v_i}{k}}$$
\end{document}


Output :  