# 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...