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Eigenvalues and eigenvectors of observables

  1. Jan 7, 2012 #1
    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. jcsd
  3. Jan 8, 2012 #2

    vela

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    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##.
     
  4. Jan 8, 2012 #3
    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
     
  5. Jan 10, 2012 #4

    vela

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