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\begin{document}

\csection{Ph 340 -- Problem Set 12 -- Spring 1997}

\begin{enumerate}
\item
In two space dimensions compute $[H,L]$, where
\begin{displaymath}
	H = (p_x^2 + p_y^2 + x^2 + y^2 )/2
\end{displaymath}
and
\begin{displaymath}
	L = x p_y - y p_x .
\end{displaymath}
(Take $\hbar = 1$.)
\item
Solve the scaled ($m , \hbar = 1$) spherical harmonic oscillator problem
\begin{displaymath}
	H = (p_x^2 + p_y^2 + p_z^2 + x^2 + y^2 + z^2 )/2
\end{displaymath}
in two ways, finding the energies and eigenstates in both cases:
\begin{enumerate}
\item
In Cartesian coordinates.
\item
In spherical coordinates.  (You need only find the results for the
ground state and the first excited state in this case.)
\end{enumerate}
\end{enumerate}

\end{document}
