- #1

goodphy

- 216

- 8

Let's have two electrons with same orbital quantum number

*l*and these electrons are in antiparallel; one electron has magnetic quantum number

_{i}*m*and and other electron has

_{i}= a*m*(but we don't know which one has

_{i}= -a*ml = a*as we're in coupled representation to talk about total angular momentum).

In this system, we know that total magnetic quantum number

*m*is zero as [tex]m = \sum\limits_i {{m_i} = 0} .[/tex]

*m*is allowed to be only

*0*so total orbital quantum number

*l = 0*(

*l = 0*allows only

*m = 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)?