% Homework for Physical Mathematics I
% Ewan Stewart
% KAIST
% 2011/12/5

\documentclass[a4paper,12pt]{article}

\usepackage{pm1}

\setcounter{homework}{9}
\setcounter{question}{2}

\begin{document}

\begin{homework}
[Optional extra question.]

\question{p}

The Hermitian operators $\hat{x}$ and $\hat{p}$ satisfy
\begin{equation} \label{com}
\left[ \hat{x} , \hat{p} \right] = i
\end{equation}
and
\begin{equation} \label{xeigen}
\hat{x} \ket{x} = x \ket{x}
\end{equation}
Express $\hat{p}$ as a differential operator $p_x$.
Calculate
\begin{equation} \label{ket}
e^{ia\hat{p}} \ket{x}
\end{equation}
and
\begin{equation} \label{fn}
e^{iap_x} \fn{\phi}{x}
\end{equation}

\end{homework}

\end{document}

