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Evaluating Operators

  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Given the operator A = d/dx and B = x and the function f(x) = xe^(-ax)

    evaluate : ABF(x) and BAF(x)

    Do these operators commute (yes/No)

    2. Relevant equations
    [A,B]F(x) = ABF - BAF = 0 ; means they commute


    3. The attempt at a solution
    [A,B]F(x) = ABF - BAF = 0
    =d/dx(x^2e^-ax) - x d/dx (xe^-ax)
    =2xe^-ax - ax^2e^-ax - xe^-ax + ax^2e^-ax
    = 2xe^-ax - xe^-ax

    No they do not commute


    [B,A]F(x) = BAF - ABF = 0
    = x d/dx(xe^-ax) - d/dx (x^2e^-ax)
    = xe^-ax - x^2ae^-ax - 2xe^-ax + x^2ae^-ax
    = xe^-ax - 2xe^-ax

    They do not commute...


    I was checking to see if my answer was right. Thanks in advance...
     
  2. jcsd
  3. Feb 11, 2015 #2

    Bystander

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    Looks good.
     
  4. Feb 11, 2015 #3

    Simon Bridge

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    Seems reasonable - but needs a cleanup.
    You should either keep the =0 all the way down (using implied signs on the left of each line) or leave it off the first line.
    You need to comment that the last line does not equal zero (or that it is false if you kept the =0 part).

    The assignment expects you to evaluate ABF and BAF separately and notice that they are not the same.
     
  5. Feb 11, 2015 #4
    Thanks you all so much for your feedback. I am very grateful:).
    GOD bless....
     
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