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Commutator Relations; Conjugate Product of a Dimensionless Operator

  1. Oct 7, 2013 #1
    Consider the following commutator for the product of the creation/annihilation operators;

    [A*,A] = (2m(h/2∏)ω)^1 [mωx - ip, mωx + ip] = (2m(h/2∏)ω)^1 {m^2ω^2 [x,x] + imω ([x,p] - [p,x]) + [p,p]}

    Since we have the identity;

    [x,p] = -[p,x]

    can one assume that..

    [x,p] - [p,x] = [x,p] - (-[x,p]) = -2[p,x]
     
  2. jcsd
  3. Oct 9, 2013 #2

    CompuChip

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    That's right.

    (And of course [x, x] = [p, p] = 0).
     
  4. Oct 10, 2013 #3
    Thanks CompuChip
     
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