Construct States from Clebsch-Gordon Coefficients

[DeldotB]

Homework Statement

Hello all,
Im asked to construct the state | \frac{5}{2} , \frac{3}{2} \rangle from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle.

Homework Equations

Clebsch Gordon Coefficient's table

The Attempt at a Solution

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To be honest, I am not sure how to get started. My book does not explain how to construct states from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle. Can anyone point me in the right direction? Thanks!

 

[blue_leaf77]

Are you asked to write an eigenstate of the total angular momentum $\mathbf{J} = \mathbf{L} + \mathbf{S}$ (which is in this case $|5/2,3/2\rangle$) in terms of the individual eigenstates of $\mathbf{L}$ and $\mathbf{S}$? If yes, the easiest way is just to look up in the table of Clebsch-Gordan coefficients which you can find online.