The key word is an electron. The total angular momentum is conserved, but the way the electrons share it between them is not. As I recall, actual atomic Hamil

The key word is an electron. The total angular momentum is conserved, but the way the electrons share it between them is not. As I recall, actual atomic Hamiltonians have terms like σ₁·σ₂. The reason involves some tricky correspondence between exchange and spin that I haven't thought about in a long time, and would have to look up. I agree with the broader point that this essay is odd and confusing.