% miko:type: atomic
% miko:title: Spin One Half
% miko:summary: The simplest intrinsically quantum angular momentum system.
% miko:tags: quantum
% miko:difficulty: undergrad
% miko:related: commutator, angular-momentum-quantum, standard-model
% miko:keywords: spinor, Pauli matrices, measurement

\documentclass{article}
\usepackage{amsmath}
\title{Spin One Half}
\begin{document}
\maketitle

\section{Pauli Matrices}

Spin-one-half operators are written

$$
S_i=\frac{\hbar}{2}\sigma_i.
$$

The Pauli matrices obey

$$
[\sigma_i,\sigma_j]=2i\epsilon_{ijk}\sigma_k.
$$

\section{Measurement}

Measurement along an axis gives only two outcomes, commonly called spin up and
spin down along that axis.

\end{document}
