# 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

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Eigenvalue Spectrum Operator Date
A Eigenvalue Problem and the Calculus of Variations Jan 8, 2018
I Eigenvalues of Circulant matrices Oct 1, 2017
I Eigenvalues of block matrices Sep 10, 2017
A Numerically Calculating Eigenvalues Aug 26, 2017
A Spectrum of linear operator Aug 10, 2016