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Raising and lowering operators

  1. May 5, 2017 #1
    1. The problem statement, all variables and given/known data
    a.jpg

    2. Relevant equations


    3. The attempt at a solution
    e.jpg

    1.1st circle on the left : where did I miss a minus sign?
    2. How to show that the last term is equal to 1?

    Thanks!
     
  2. jcsd
  3. May 5, 2017 #2

    TSny

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    Gold Member

    I don't think you missed a minus sign here.
    You'll have to see if it is, in fact, equal to 1.

    You could try expanding the two exponentials in your question-mark expression and see if you can simplify it. Think about what happens when you act on the ground state with powers of a followed by powers of a.
     
  4. May 5, 2017 #3
    Thanks, after expanding the exponential I recover the minus sign:smile:.
     
  5. May 5, 2017 #4

    TSny

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    OK, good.
     
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