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Diarac notation

  1. Nov 28, 2011 #1
    I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy.

    I started with Eigenvaluee problem H|Psi> = E|psi>

    H = ? for state a?

    SO it means that indvdually H= E (|a><a|) for state a
    and for all three states i can write
    H= E (|a><a|+|b><b|+|c><c|)

    am i right?
     
    Last edited: Nov 28, 2011
  2. jcsd
  3. Nov 28, 2011 #2

    dextercioby

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    H = E(|a><a|+...) would be a hint.
     
  4. Nov 28, 2011 #3
    SO it means that indvdually H= E (|a><a|) for state a
    and for all three states i can write
    H= E (|a><a|+|b><b|+|c><c|)

    am i right?
     
  5. Nov 28, 2011 #4

    A. Neumaier

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    Re: Hamiltonian in Dirac notation

    The H you want is most likely a 3x3 matrix. If your states a, b c are orthogonal eigenstates, the energies are the diagonal entries and the off-diagonal entries were zero. In Dirac notation, this is
    H= E_a|a><a|+E_b|b><b|+E_c|c><c|

    But only if the eignestates are orthogonal and eigenstates!!!
     
  6. Nov 29, 2011 #5
    So if states are degenerate i can have

    H= [E_a 0 0 psi = [a
    0 Eb 0 b
    0 0 EC] c]
     
  7. Nov 30, 2011 #6

    A. Neumaier

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    Your equation looks garbled. Please use an intelligible format, to be able to answer your question.
    (Probably the answer to your question is yes, but since the question isn't clear, the answer cannot be.)
     
  8. Nov 30, 2011 #7
    H= [E_a 0 0 ; 0 E_b 0; 0 0 E_c]

    Psi= [a; b;c]
     
  9. Nov 30, 2011 #8

    A. Neumaier

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    Yes, this is meaningful. The formula for H says that you represent the Hamiltonian in an eigenbasis, and the formula for psi says that the state you consider decomposes in this eigenbasis with coefficients a, b, and c.
     
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