The eigenvalue of the operator \(\hat{S}_x^2+\hat{S}_y^2\) in the state \(\left|S, m_s\right\rangle=\left|\frac{1}{2}, \frac{1}{2}\right\rangle\) is (Here symbols and notations have their usual meanings)
1
\(2 \hbar^2\)
2
\(\hbar^2\)
3
\(\frac{\hbar^2}{2}\)
4
\(\frac{\hbar^2}{4}\)
5
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