Solution to 1996 Problem 52

The normalized eigenfunctions for a rigid rotator that is free to rotate about its center of mass in three dimensions are the spherical harmonics Y_l^m. (See Griffiths QM Problem 4.24). The given wave function can be expanded in terms of the spherical harmonics as follows

\begin{align}\Psi(\theta,\phi) = \frac{1}{\sqrt{2}}\left(-i Y_1^{+1} + i Y_1^{-1}\right)\end{align}
Therefore, measurement of L_z will yield m = +1 or m = -1, which corresponds to \hbar or -\hbar. Therefore, answer (C) is correct.

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