% miko:type: atomic
% miko:title: Infinite Square Well
% miko:summary: The canonical example of quantization from boundary conditions.
% miko:tags: quantum
% miko:difficulty: undergrad
% miko:related: schrodinger-equation, wavefunction-normalization
% miko:keywords: boundary condition, energy level, eigenfunction

\documentclass{article}
\usepackage{amsmath}
\title{Infinite Square Well}
\begin{document}
\maketitle

\section{Setup}

For $0<x<a$ and infinite walls at the boundaries, the wavefunction satisfies

$$
\psi(0)=\psi(a)=0.
$$

\section{Solutions}

The normalized stationary states are

$$
\psi_n(x)=\sqrt{\frac{2}{a}}\sin\left(\frac{n\pi x}{a}\right),
$$

with energies

$$
E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}.
$$

\end{document}
