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Fundamental characteristic property of particles which together with orbital angular momentum acts as the generator of rotations and which doesn't have a classical equivalent but is sometimes compared to and contrasted with classical intrinsic angular momentum.
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Describing a subspace of a Hilbert space of $N$ spins 1/2
Consider having $N$ spins $1/2$, so the overall state of $N$ particles can be described by the total spin value $S=0 \ldots N/2$ (let us set $N$ to be even for simplicity), and the projection of the t …