- #1

gfd43tg

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## Homework Statement

## Homework Equations

## The Attempt at a Solution

For a angular momentum ##J##, there exists the eigenvalue problems

$$J^{2} \mid j \hspace{0.02 in} m \rangle = j(j +1)\hbar^{2} \mid j \hspace{0.02 in} m \rangle $$

$$ J_{z} \mid j \hspace{0.02 in} m \rangle = m \hbar \mid j \hspace{0.02 in} m \rangle $$

(a)

So I will plug in the values to get me started with this position and spin state

$$ \frac {1}{\sqrt{24}} a^{-3/2} \frac {r}{a} e^{-r/2a} \Big [ \sqrt {\frac {1}{4 \pi}} cos \hspace{0.02 in} (\theta) \begin{pmatrix} 1 \\ 0 \end{pmatrix} - \sqrt {\frac {1}{4 \pi}} sin \hspace{0.02 in} (\theta) \hspace{0.02 in} e^{i \phi} \begin{pmatrix} 0 \\ 1 \end{pmatrix} \Big ] $$

But I have no clue what theta, phi, or r are supposed to be, or what I should do from here if this is even the correct first step.

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