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Its frequently written in my QM book that there can be two electrons in every state, one spin up and one spin down. Where does this come from? My book seems to take it as an axiom.

If we have a He atom with its electrons in the singlet state. Then as I understand it the wave function will be something like this

U = f(u,v) |0 0> where f is symmetric since |0 0> isnt.

Since electrons are fermions I take it that this must imply that f(r,r) = 0 for all r? If this is the case, is it known what order of zero f(r,r) is?

eg. f(u,v) = g(u,v)*(u-v)^n what then is n in the He case if g(r,r)<>0.

If we have a He atom with its electrons in the singlet state. Then as I understand it the wave function will be something like this

U = f(u,v) |0 0> where f is symmetric since |0 0> isnt.

Since electrons are fermions I take it that this must imply that f(r,r) = 0 for all r? If this is the case, is it known what order of zero f(r,r) is?

eg. f(u,v) = g(u,v)*(u-v)^n what then is n in the He case if g(r,r)<>0.

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