Is Total Angular Momentum J=L+s or J=L1+L2?

[rubertoda]

HI,i am aiming to show that 1/(2)^1/2(|spin up>|spin down> + |spin down>|spin up>) is an eigenvalue to the total angular momentum operator in a two-electron system.


I know that i should end up with getting the eigenvalues of the separate spins; L1|spin up> and
L2|spin down> and so on..also i have been suggested to use L+ and L- operators...anyone who can help how to start with the solution? thanks a lot!

Do they mean the total angular momentum to be J=L+s OR L1 + L2??

 

[Oxvillian]

I think the operator in question would be
$$S^2 = ({\bf S_1} + {\bf S_2})^2.$$
Try operating on your state with that. You'll need to express the crossterm in terms of ladder operators.

 

[rubertoda]

Thanks. But wouldn't the total angular momentum operator be like, L or J? I mean, not the total spin operator?


kind regards

 

[Oxvillian]

I think when they say "total" here, they're talking about the total spin angular momentum S₁ + S₂. Not the spin angular momentum plus the orbital angular momentum.