Solution to 1992 Problem 28

The eigenstates with m = 3 are Y_l^3 where l \geq 3. Therefore, the desired probability is
\begin{align*}\sum_{l = 3}^{\infty} \left|\int \left(Y_l^3\right)^* \psi(\theta, \phi)\right|^2\end{align*}
Using the fact that the spherical harmonics are orthogonal and normalized, this reduces to
\begin{align*}&\left|\int \left(Y_4^3\right)^* \psi(\theta, \phi)\right|^2 + \left|\int \left(Y_6^3\right)^* \psi(\theta,...
Therefore, answer (E) is correct.

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