# Spin,orbital and total angular momentum

1. Mar 14, 2013

### ShayanJ

In the section "Angular momentum in quantum mechanics" of the angular momentum page in wikipedia,one can find the following:
But we know that spin is an intrinsic property of a particle,a property that can be used for its identification.So how is it that it is not conserved?
I mean,we say that e.g. electrons' spin is 1/2.If spin is not conserved,then what is this 1/2?

Thanks

2. Mar 14, 2013

### Staff: Mentor

The magnitude of the spin angular momentum is fixed:

$$S = \sqrt{s(s+1)} \hbar = \sqrt{\frac{1}{2} \left( \frac{1}{2}+1 \right)} \hbar = \frac{\sqrt{3}}{2} \hbar$$

but the component along any direction (usually we call it the z-direction) can change:

$$S_z = m_s \hbar = \pm \frac{1}{2} \hbar$$

that is, it can be either "spin up" or "spin down".

3. Mar 15, 2013

### Meir Achuz

In J=L+S, the S can be the total spin of several electrons. The 1/2 spin of each electron can add up to different spin S values.