Explain Spin-Orbit Coupling for d Orbital l=2

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SUMMARY

This discussion focuses on understanding spin-orbit coupling specifically for d orbitals (l=2) and the calculation of Clebsch-Gordan coefficients. The highest state is represented as |5/2, 5/2> = uY_2^2, where 'u' denotes up spin. The lowering operator is defined as J_- = L_+S_, which is essential for deriving the states of the electron in the d orbital. A clear grasp of these concepts is crucial for accurate calculations in quantum mechanics.

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chill_factor
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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.
 
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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.
 

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