The normalized wave function of an electron is
\(\psi(\vec{r})=R(r)\left[\sqrt{\frac{3}{8}} Y_1^0(\theta, \varphi) \chi_{-}+\sqrt{\frac{5}{8}} Y_1^1(\theta, \varphi) \chi_{+}\right]\),
where \(Y_l^m\) are the normalized spherical harmonics and X± denote the wavefunction for the two spin states with eigenvalues ±\(\frac{1}{2}\) h. The expectation value of the z component of the total angular momentum in the above state is
1
-\(\frac{3}{4} \)h
2
\(\frac{3}{4} \)h
3
-\(\frac{9}{8} \)h
4
\(\frac{9}{8} \)h