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Operators and Commutators help

  1. Oct 18, 2011 #1
    Hi, I have this quesiton for a problem sheet:

    Use the unit operator to show that a Hermitian operator A can be written in terms of its orthonormal eigenstates ln> and real eigenvalues a as :

    A=(sum of) ln>a<nl

    and hence deduce by induction that A^k = (sum of) ln>a^k<nl

    I have no idea where to begin and was wondering if someone could give me some pointers and help me work through it. Also, sorry about my notation

    Thanks :)
     
  2. jcsd
  3. Oct 18, 2011 #2
    You are probably assumed to know that [tex]1 = \sum_n |n\rangle \langle n|[/tex], where 1 means the unit operator.
     
  4. Oct 18, 2011 #3
    Yes we are, sorry it says that as well. Any pointers on where to begin still?
     
  5. Oct 18, 2011 #4
    Sure, but I think it's rather obvious as the question already says is: A = 1A = A1 (that's the definition of the unity operator, btw).
     
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