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## Main Question or Discussion Point

I am trying to self-learn quantum mechanics pertaining to Lanthanide ions.

For a given set of J and MJ quantum numbers in a valence 4f^2 electronic configuration, J=0,2,4,6 and MJ=0,6,-6. The |J,MJ> basis functions are |0,0>, |2,0>, |4,0>, 1/2[|6,6>+|6,-6>]+sqrt(1/2)|6,0>, and 1/2[|6,6>+|6,-6>]-sqrt(1/2)|6,0>. I understand that the MJ quantum number goes from 0,1,2,... to J. I am guessing that the coefficients 1/2 and sqrt(1/2) are Clebsch-Gordon coefficient?

Can someone explain how the |J,MJ> basis functions are obtained for J=6 and MJ=0,6,-6? Please refer me to a book or a website where I could understand better on this subject. Thank you.

For a given set of J and MJ quantum numbers in a valence 4f^2 electronic configuration, J=0,2,4,6 and MJ=0,6,-6. The |J,MJ> basis functions are |0,0>, |2,0>, |4,0>, 1/2[|6,6>+|6,-6>]+sqrt(1/2)|6,0>, and 1/2[|6,6>+|6,-6>]-sqrt(1/2)|6,0>. I understand that the MJ quantum number goes from 0,1,2,... to J. I am guessing that the coefficients 1/2 and sqrt(1/2) are Clebsch-Gordon coefficient?

Can someone explain how the |J,MJ> basis functions are obtained for J=6 and MJ=0,6,-6? Please refer me to a book or a website where I could understand better on this subject. Thank you.

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