- #1

jcharles513

- 22

- 0

## Homework Statement

Consider the so-called Spin Hamiltonian

H=AS

^{2}

_{Z}+B(S

^{2}

_{X}-S

^{2}

_{Y})

for a system of spin 1. Show that the Hamiltonian in the S

_{Z}basis is the 3x3 matrix:

\hbar

^{2}*[(A,0,B; 0,0,0; B,0,A)].Find the eigenvalues using degenerate pertubation theory.

## Homework Equations

Spin Pauli Matrices

## The Attempt at a Solution

I don't know where to start with this since the Pauli Matrices I know are 2x2 matrices. How did the Hamiltonian become a 3x3. What am I missing? Can someone get me started?