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I have this Hamiltonian:

[itex] \mathcal{H} = \alpha S_{+} + \alpha^{*}S_{-} + \beta S_{z} [/itex]

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

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

This Hamiltonian describes anisotropy of g-factor.

Thanks

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# Eigenvalue Spectrum of this Operator

Can you offer guidance or do you also need help?

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