If, say, the z-spins of two electrons are maximally entangled (so that their composite state can be given by $|\Psi\rangle = \frac{1}{\sqrt{2}}(|u\rangle|d\rangle + |d\rangle|u\rangle)$, how do you compute the total spin of the system (or each component of the system)?
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$\begingroup$ The components alone would not be well-defined. The total spin of the entire system is known by definition. The state you wrote down is a spin 1 in the Sz=0 state. $\endgroup$– naturallyInconsistentCommented Apr 19, 2023 at 15:33
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1$\begingroup$ To compute it, act with the total spin operators $\hat{S}_z=\hat{S}_{1,z}+\hat{S}_{2,z}$; and $\hat{S}^2=\hat{\vec{S}}\cdot\hat{\vec{S}}=(\hat{\vec{S}}_1+\hat{\vec{S}}_2)\cdot(\hat{\vec{S}}_1+\hat{\vec{S}}_2)$ (which can be written in terms of $\hat{S}_{j,z}$'s and $\hat{S}_{\pm,z}$'s. $\endgroup$– marchCommented Apr 19, 2023 at 15:46
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