# Helium Spin Triplet

## Main Question or Discussion Point

For the ortho state of Helium, the spin part of the wavefunction is symmetric.

There are 3 possible symmetric wavefunctions we can construct from the 2 electrons' spins.

(^^)

(vv)

[1/SQRT2] { (^v) + (v^) }

I am confused as to why this last state gives a total spin of one? The electrons can only be in one of these eigenstates, both of equal probability of 1/2, but the spins are anti-aligned, are they not???

Thanks guys! (I hope you'll not mind my improvisation for electron spin functions with ^ and v !! :tongue: )

Cheers!

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dextercioby
Homework Helper
For the ortho state of Helium, the spin part of the wavefunction is symmetric.

There are 3 possible symmetric wavefunctions we can construct from the 2 electrons' spins.

(^^)

(vv)

[1/SQRT2] { (^v) + (v^) }

I am confused as to why this last state gives a total spin of one? The electrons can only be in one of these eigenstates, both of equal probability of 1/2, but the spins are anti-aligned, are they not???

Thanks guys! (I hope you'll not mind my improvisation for electron spin functions with ^ and v !! :tongue: )

Cheers!
1. Learn to write with LaTeX code. $$\left|\uparrow\downarrow\right\rangle$$ - it looks so pretty ! :!!)

2. Well, to find the spin of a certain state, you must apply the total angular momentum operator squared. When you do that, you'll get the spin 1.

Remember that it's not $\mbox{m}_{\mbox{j}}$ who gives the spin of the state, but $\mbox{j}$.

Ah, an oversight on my part! Thanks for clearing that up!