- #1

ghostflame

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## Homework Statement

Find the energy levels of a 2-spin 1/2 system with spinoperators S1 and S2 in an external magnetic field. The hamiltonian is of the form,

H= A ( 1-[tex]\frac{2S_{1}}{h}[/tex] . [tex]\frac{2 S_{2}}{h}[/tex] )+ [tex]\frac{\mu B}{h}[/tex](S[tex]_{1,z}[/tex]+S[tex]_{2,z}[/tex])

The h is a h-bar, constants A, B, and S1 and S2 the spin operators

## Homework Equations

I have to solve the equation H l[tex]\psi[/tex]> = El[tex]\psi[/tex]>

## The Attempt at a Solution

The spin system is has a basis, l[tex]\uparrow\uparrow>,\left| \uparrow\downarrow>,\left|\downarrow\uparrow>,\left|\downarrow\downarrow>[/tex]

so any [tex]\left| \psi[/tex]> is a linear combination of the basis above, but i don't know how i can calculate the eigenvalues of the above equation. I have a feeling i have to use the Pauli matrices but iam not sure. Anyone has an idea? It should be a 3 level system...