Explain Spin-Orbit Coupling for d Orbital l=2

[chill_factor]

Can someone explain to me how to get the states for an electron in a given orbital (lets say... d orbital l=2) and how to calculate the Clebsch-Gordan Coefficients for this system? I tried reading my book but I'd like someone to explain in simpler language.

 

[Meir Achuz]

Start with the highest state (with u for up spin and d for down spin):
|5/2,5/2>=uY_2^2. The use the lowering operator J_-=L_+S_.
You do have to know about lowering operators.