% miko:type: atomic
% miko:title: Wavefunction Normalization
% miko:summary: The total probability associated with a quantum state must equal one.
% miko:tags: quantum
% miko:difficulty: undergrad
% miko:related: schrodinger-equation, commutator, time-evolution-operator
% miko:keywords: probability, Hilbert space, quantum state

\documentclass{article}
\usepackage{amsmath}
\title{Wavefunction Normalization}
\begin{document}
\maketitle

\section{Condition}

For a single particle wavefunction,

$$
\int_{\mathbb R^3} |\psi(\mathbf r,t)|^2\,d^3r = 1.
$$

\section{Meaning}

$|\psi|^2$ is a probability density. Normalization makes the probabilistic
interpretation consistent.

\end{document}
