Question

The electron in a hydrogen atom occupies the combined spin and position state $$R_{21}\left(\sqrt{\frac{1}{3}} Y_{1}^{0} \chi_{+}+\sqrt{\frac{2}{3}} Y_{1}^{1} \chi_{-}\right)$$ (a) If you measured the orbital angular momentum squared $\left(L^{2}\right)$, what values might you get. and what is the probability of each? (b) Same for the $z$ -component of orbital angular momentum $\left(L_{z}\right)$. (c) Same for the spin angular momentum squared $\left(S^{2}\right)$. (d) Same for the $z$ -component of spin angular momentum $\left(S_{z}\right)$. Let $\mathbf{J} \equiv \mathbf{L}+\mathbf{S}$ be the total angular momentum. (e) If you measured $J^{2}$, what values might you get, and what is the probability of each? (f) Same for $J_{2}$.

          The electron in a hydrogen atom occupies the combined spin and position state
$$R_{21}\left(\sqrt{\frac{1}{3}} Y_{1}^{0} \chi_{+}+\sqrt{\frac{2}{3}} Y_{1}^{1} \chi_{-}\right)$$
(a) If you measured the orbital angular momentum squared $\left(L^{2}\right)$, what values might you get. and what is the probability of each?
(b) Same for the $z$ -component of orbital angular momentum $\left(L_{z}\right)$.
(c) Same for the spin angular momentum squared $\left(S^{2}\right)$.
(d) Same for the $z$ -component of spin angular momentum $\left(S_{z}\right)$. Let $\mathbf{J} \equiv \mathbf{L}+\mathbf{S}$ be the total angular momentum.
(e) If you measured $J^{2}$, what values might you get, and what is the probability of each?
(f) Same for $J_{2}$.

Added by Cindy P.

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