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Operator and Dirac Algebra

  1. Aug 28, 2014 #1
    Hi Guys, I am facing a problem playing around with some operators and Kets, would like some help!

    I have [tex]\langle \Psi | A+A^\dagger | \Psi \rangle .A [/tex]

    Could someone simplify it? Especially is there a way to change the last operator A into A^\dagger?

    The way I thought about this is:
    [tex]
    =(\langle \Psi |A | \Psi \rangle + \langle \Psi | A^\dagger | \Psi \rangle).A
    =(\langle \Psi |A A | \Psi \rangle + \langle \Psi | A^\dagger A | \Psi \rangle)
    =\langle \Psi | I | \Psi \rangle
    [/tex]
     
  2. jcsd
  3. Aug 28, 2014 #2

    bhobba

    Staff: Mentor

    That's obviously wrong.

    You have a scalar times an operator and you get a scalar.

    You cant take the operator inside the bra-ket.

    Off the top of my head you might like to expand A in terms of the spectral theorem ie ∑ ai |bi><bi| - assuming it applies of course.

    Thanks
    Bill
     
    Last edited: Aug 28, 2014
  4. Aug 28, 2014 #3
    Thanks Bill. Actually there is a detail that I omitted which may help:
    (⟨Ψ|A|Ψ⟩+⟨Ψ|A†|Ψ⟩).A|Ψ⟩
    Does this make any difference?

    thanks
     
  5. Aug 28, 2014 #4

    bhobba

    Staff: Mentor

    Same problem - only you have a scalar times a vector.

    Thanks
    Bill
     
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