# Eigenvalue Spectrum of this Operator

1. Mar 19, 2012

### Joschua_S

Hello

I have this Hamiltonian:

$\mathcal{H} = \alpha S_{+} + \alpha^{*}S_{-} + \beta S_{z}$

with $\alpha, \beta \in \mathbb{C}$. The Operators $S_{\pm}$ are ladder-operators on the spin space that has the dimension $2s+1$ and $S_{z}$ is the z-operator on spin space.

Do you know how to get (if possible with algebraic argumentation) the eigenvalue spectrum $\sigma( \mathcal{H} )$?

This Hamiltonian describes anisotropy of g-factor.

Thanks
Greetings