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\Large\centerline{\bf Central Forces}
\normalsize\centerline{\bf Spherical Harmonic Series}
\bigskip
Consider the following normalized abstract quantum state on a sphere:

\begin{equation*}
\psi(\theta,\phi)=\left(\dfrac{15}{16 \pi}\right)^{\frac{1}{2}}\sin{\left(2\theta\right)}\sin{\phi}.
\end{equation*}

This function can also be written as a series of spherical harmonics:
\begin{equation*}
\psi(\theta,\phi)=\sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell} c_{\ell,m}Y_{\ell,m}(\theta,\phi).
\end{equation*}

\begin{enumerate}
\item Each group will be assigned one coefficient for this series (\emph{e.g.} $c_{0,0}, c_{1,0}, c_{1,1}$) to calculate.
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\item What is one thing you've learned from this activity that you want  to remember?

\end{enumerate}

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\leftline{\it by Corinne Manogue, Mary Bridget Kustusch}
\leftline{\copyright 2012 Corinne A. Manogue}
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