# L-S coupling

1. Jan 26, 2005

### secret2

When doing L-S coupling scheme for (3d)4, I am asked to find the ground state. I know that the first step, according to Hund's rules, is to find the the S with the largest value (S, L are total values, s, l are individual values). It is obviously S=2. Next, I should proceed to find the largest possible value of L. And here is my question: why can't we choose L=4*2=8? Why should we choose L=2?(Please continue reading)

The book says that anything larger than L=2 would have values of (m (sub L)) larger than 2, which is prohibited by the Pauli exclusive principle because no two electrons can have same pair of (m (sub l)) and (m (sub s)). However, why do we have to throw away the whole set of states with a specific L just because some (m (sub L)) are illegal?

2. Jan 29, 2005

### dextercioby

Well,each time u have an "L",u have the "2L+1" values of "m" to go along...Now if L=3,then in principle m_{l}=3 (okay?).But if u cannot have m_{l}=3,then it would make no sense in including the L=3 (which automatically would induce m_{l}=3)...

Daniel.

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