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Homework Help: Commutator math help

  1. Feb 19, 2008 #1
    Does the relation [itex][f(\hat{A}),\hat{B}] = df(\hat{A})/d\hat{A}[/itex] follow when A commutes with [A,B]? or is this only valid when [A,B]=1?
     
  2. jcsd
  3. Feb 19, 2008 #2

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    If A commutes with [A,B] then:

    [tex] [f(A),B] = [A,B] f'(A) [/tex]

    You should try to derive this formula. Use a taylor expansion of f(A), ie:

    [tex]f(A) = f(0) + f'(0) A + \frac{1}{2} f''(0) A^2 + ... [/tex]
     
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