Consider the possible values of S and L for carbon configuration 1s22s22p2 and the corresponding rapresentations with arrows indicating the spins (consider only S=0,L=0 and S=0,L=2, as for S=1,L=1 some are missing).
I can't understand which one of the two representations indicated in red belong to S=0,L=0 state and which one to the S=0,L=2 state (I took a guess making the picture).
The spin wavefunction is in all cases antysymmetric (S=0) and equal to χ=(|↑1↓2⟩−|↓1↑2⟩)÷√2
Therefore the spatial wavefunction (L) must be symmetric for Pauli principle and in the second red configuration is
Ψ=p0(1)p0(2) in the first one is
Ψ=[p−(1)p+(2)+p+(1)p−(2)]÷√2
The wavefunctions are different so there must be a difference between the two red configurations, but which of them should belong to S=0,L=2 and the other to S=0,L=0 and why?
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