% miko:type: atomic
% miko:title: Quantum Angular Momentum
% miko:summary: The operator algebra that controls orbital and spin angular momentum.
% miko:tags: quantum
% miko:difficulty: undergrad
% miko:related: commutator, spin-one-half, schrodinger-equation
% miko:keywords: angular momentum, eigenvalues, ladder operators

\documentclass{article}
\usepackage{amsmath}
\title{Quantum Angular Momentum}
\begin{document}
\maketitle

\section{Algebra}

Angular momentum operators satisfy

$$
[J_i,J_j]=i\hbar\epsilon_{ijk}J_k.
$$

\section{Eigenvalues}

The simultaneous eigenstates of $J^2$ and $J_z$ obey

$$
J^2|jm\rangle=\hbar^2j(j+1)|jm\rangle,
\qquad
J_z|jm\rangle=\hbar m|jm\rangle.
$$

\end{document}
