Hund's rule and angular momentum coupling

daudaudaudau

Hi.

In Hund's second rule, it seems that we calculate the value of L simply by summing the $L_z$ components of the individual electrons. But L has to do with the eigenvalue of the L^2 operator, i.e. the eigenvalue is L(L+1). So how can this be correct?

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Meir Achuz

Homework Helper
Gold Member
L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.

daudaudaudau

L is the maximum eigenvalue of L_z.
L(L+1) is the eigenvalue of a different operator, L^2.
Yeah that is exactly my point. We know that that L_z has some particular value. Now why is L=L_z ?

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