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Product of two exponentials of different operators

  1. Jul 10, 2015 #1
    How does one show that
    eAeB=eA+Be[A,B]/2
    where A,B are operators and [ , ] is the commutator. The QM book I am using states it as a fact without proof, but I would like to see how it is proved. I've muddled around with the series expansion, but can't get farther than a few term by term products which lead nowhere.
     
  2. jcsd
  3. Jul 10, 2015 #2

    DrDu

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    Science Advisor

    Search for ."Baker-Campbell-Hausdorf" formula.
     
  4. Jul 10, 2015 #3
    Do note that the formula only works if A and B commute with [A,B]. I think ther eis a proof in the Cohen-Tannoudji book
     
  5. Jul 11, 2015 #4
    Its in Sakurai's Modern Quantum Mechanics and indeed its Baker-Campbell-Hausdorf formula.
    If i remember good then there is a proof or at least a partial proof in Sakurai.
     
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