Eigenvalues and eigenvectors of observables

1. Jan 7, 2012

Fixxxer125

1. The problem statement, all variables and given/known data

Calculate the Eigenvalues and eigenvectors of
H= 1/2 h Ω ( ]0><1[ + ]1><0[ )

2. Relevant equations

I know H]λ> = λ]λ>

3. The attempt at a solution
I don't know if I am meant to concert my bra's and ket's into matrices, and if so how to represent these as matrices?

2. Jan 8, 2012

vela

Staff Emeritus
Let me make your post look a bit prettier:
Are the states $| 0 \rangle$ and $| 1 \rangle$ orthonormal? If so, just calculate the matrix elements $\langle i |\hat{H}|j \rangle$.

3. Jan 8, 2012

Fixxxer125

Thanks! In the solution given the Eigenstates are given in terms of the |0⟩ and |1⟩ states in the Hamiltonian. How do I know what these states are in terms of matrices so I can write the eigenstates in terms of these? Cheers

4. Jan 10, 2012

vela

Staff Emeritus
Those two states are the basis you're using, so...