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Let's have two electrons with same orbital quantum numberland these electrons are in antiparallel; one electron has magnetic quantum number_{i}mand and other electron has_{i}= am(but we don't know which one has_{i}= -aml = aas we're in coupled representation to talk about total angular momentum).

In this system, we know that total magnetic quantum numbermis zero as [tex]m = \sum\limits_i {{m_i} = 0} .[/tex]mis allowed to be only0so total orbital quantum numberl = 0(l = 0allows onlym = 0). This is exact the same problem about total angular momentum for a closed shell in an atom.

So...can I simply conclude that total angular momentum (and also spin) is always zero for antiparallel electrons (antiparallel-spin electrons)?

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# I Total angular momentum for antiparallel electrons

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