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## Homework Statement

The Hamiltonian H for a certain physical quantum mechanical system has three eigenvectors {|v1>, |v2>, |v3>} satisfying:

H|v

_{j}> = (2-j)a|v

_{j}>

Write down the matrix representing H in the representation {|v1>, |v2>, |v3>} .

## Homework Equations

## The Attempt at a Solution

I though the Hamiltonian would just be the eigenstates along the diagonal, however this seems too simple.

a 0 0

0 0 0

0 0 -a

a 0 0

0 0 0

0 0 -a