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I QM - Ladder Operator QHO - factorization

  1. May 16, 2016 #1
    Hi, quick question with A being the lowering operator and A the raising operator for a QHO

    (A A - 1 + 1/2) ħω [Aψ] = A (A A - 1 + 1/2) ħω ψ

    By taking out a factor of A. Why has the ordering of A A swapped around? I would have thought taking out a factor of A would leave it as

    A (A - 1 + 1/2) ħω ψ

  2. jcsd
  3. May 16, 2016 #2


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    There is another A in [Aψ]. Pull this A in to the bracket from the right to get (AAA - A + 1/2A). Now pull out A out to the left of the bracket.
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