# Raising operator for s in |s,m> states

1. Feb 17, 2015

### lfqm

Are there any known (collective spin) operators to raise or lower the quantum number s in $$\left|{s,m}\right>$$ spin states?

I'm trying to construct coherent states varying the quantum number s instead of the well known spin coherent states varying m.

I found a coherent-like state similar to the one I'm looking for:
$$\left|{\psi}\right>= \displaystyle\sum_{j\geq{\left |{m}\right |}}^{N/2} Y(j) \left|{j,m}\right>$$
where Y(j) has to do with the number of young tableaux associated with j and N is the number of spin 1/2 particles we are considering. But I haven't been able to find a reference about it.

Any help will be appreciated.

2. Feb 18, 2015

### vanhees71

That's an interesting question. Googling gave this unpublished Word document, dealing with this question for orbital angular momentum. I've not checked it, but unpublished Word documents are quite suspicious usually. Perhaps it helps you to start your own research, anyway:

http://arxiv.org/abs/0912.5146

3. Feb 18, 2015

### Staff: Mentor

This has been published in the International Journal of Theoretical Physics.

4. Feb 18, 2015

### vanhees71

Great! In addition to be more credible, it's far better readable than this awful (typographically wise, I mean) Word document :-)).