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## Homework Statement

An ion has effective spin ħ. The spin interacts with a surrounding lattice so that: H

_{spin}= A S

^{2}

_{z}.

I first had to write H as a matrix. Then i had to find the energy eigenvalues.

## Homework Equations

## The Attempt at a Solution

I figured j=1 and mj = 1,0,-1

S

^{2}

_{z}= ħ

^{2}(1 0 0; 0 0 0; 0 0 1)

H=Aħ

^{2}(1 0 0; 0 0 0; 0 0 1)

I think this is right so far but do not know how to progress further. Any help would be appreciated.