Two particles with parallel spins?

[center o bass]

Hi! If we consider composite systems of two spinning particles in a box we find that there are states where the total spin add such that
$$s = s_1 + s_2$$

but where the projection of the spin along the z-axis can vary. For example the spin state

$$|s,s-2\rangle = a |s_1,s_1 -2 \rangle \otimes |s_2,s_2\rangle + b |s_1,s_1-1\rangle \otimes |s_2,s_2-1\rangle + c |s_1,s_1 - 2 \rangle \otimes |s_2,s_2\rangle$$

is such a state. As I have understood it one can understand such states where the total spin just add as states for which the spins of the two particles are parallel. However there arises a question for how two spins can be parallell when one of the particles does not have all it's angular momenta along the z-axis.. For if we were to make a mesurement on this state above we would have a possibility to find that the particles were in the state

$$|s_1,s_1 - 2 \rangle \otimes |s_2,s_2\rangle.$$

Here the two total spins add, but the z-component of the particle 2 spin is tipped of two units away from the z-axis. How can we understand these states to be parallel?

 

[Bill_K]

As I have understood it one can understand such states where the total spin just add as states for which the spins of the two particles are parallel.

This is incorrect. The states of highest total spin are only just that. There is no implication that it happens because anything is parallel.