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Baker–Campbell–Hausdorff equation

  1. Nov 21, 2015 #1
    • Poster has been reminded to use the HH Template when posting schoolwork questions here
    I have a question about Baker–Campbell–Hausdorff identity in QM: exp(X)*exp(Y) = exp(X + Y + [X,Y]/2)
    I have exp(X + Y) where X and Y don't commute and want to try to write in multiplication form. Tried adding and subtracting commutator term: exp(X + Y + [X,Y]/2 - [X,Y]/2), but now I am not sure whether identity still holds: exp(X + Y + [X,Y]/2 - [X,Y]/2) =? exp(X + Y)*exp(- [X,Y]/2) .
     
  2. jcsd
  3. Nov 22, 2015 #2

    blue_leaf77

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    Do you have further knowledge about [X,Y], i.e. whether it equals to another operator or just a number instead?
     
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