# Two particles with parallel spins?

1. Oct 8, 2011

### 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?

2. Oct 9, 2011

### Bill_K

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