QM - Ladder Operator QHO - factorization

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  • Thread starter JaneHall89
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  • #1
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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

Jane
 

Answers and Replies

  • #2
blue_leaf77
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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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