1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating exponent to get delta function

  1. Aug 9, 2014 #1
    Something i ran into while doing hw

    1. The problem statement, all variables and given/known data
    starting with
    [tex]\int{dx} e^{-ikx}\delta(x) = 1[/tex]
    we conclude by fourier theory that
    [tex]\int{dk} e^{+ikx} = \delta(x)[/tex]
    Now, i try to compute
    [tex]\int{dk} e^{-ikx}[/tex]

    (I've dropped the normalization factors of [tex]2\pi[/tex]. I beleive no harm is done by that)

    2. Relevant equations



    3. The attempt at a solution
    Method 1: change x to -x
    [tex]\int{dk} e^{-ikx} = \int{dk} e^{+ik(-x)} = \delta(-x) = \delta(x)[/tex]

    Method 2: change the integration parameter k to -k
    [tex]\int{dk} e^{-ikx} = -\int{dk} e^{+ikx} = -\delta(x)[/tex]

    So what did I do wrong here?


    thanks a lot
    T
     
  2. jcsd
  3. Aug 9, 2014 #2
    I looked at it again. At my second method. I had to change the integral limits as well, and that fixes it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integrating exponent to get delta function
Loading...