9.27 Suppose that a rotator is in the state \( Y_{1}^{-1} \). What values will measurement of \( \hat{L}_{x} \) find and with what probability will these values occur? (Hint: Most of the analysis in the text \( [(9.92) \) et seq. \( ] \) involving the expansion of the state \( Y_{1}^{1} \) may be used here.)