Adding Two Spins: A Guide to Vector Quantities

[Quarlep]

Spin is a quantity of vector but I don't know how to add them ? Please be simple
Thanks

 

[Einj]

I don't know if that's simple enough, but in QM spin is not an ordinary vector. In general, in QM when you have two systems (say two particles) represented by $|\psi_1\rangle$ and $|\psi_2\rangle$, the total state composed by the two particles is given by their tensor product: $|\psi_{tot}\rangle=|\psi_1\rangle|\psi_2\rangle$.

The same thing is valid for spins. If you have two particles with, for example, spins $S_1=1/2$ and $S_2=1/2$, then the total spin $S=S_1+S_2$ is given by the tensor product $|S\rangle=|S_1,S_{1z}\rangle|S_2,S_{2z}\rangle$, where $S_{iz}$ is the value of the third component of the i-th spin. To do this composition you need the so called Clebsch-Gordan coefficients. Anyway, the final spin can be $S=0,1$ and the value of its third component is given by this tables.

This is very very shortly explained but I hope is clear enough.

 

[Quarlep]

Yeah its clear enough thanks