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Fourier transforms

  1. Apr 19, 2010 #1
    My teacher worked out the following and said it's a unitary transformation (how?) of exp(ikx). He said we're supposed to find the periodic bounds of integration - but I thought for Fourier transforms the bounds are negative infinity to infinity, so in this case shouldn't it just be the Dirac delta function? Also, how do you get the 2 in front of the sin? When I rewrite using Euler's identity, there is no 2.

    [tex]
    \int e^{ik(x-x')}dk=\frac{e^{ik(x-x')}}{i(x-x')}\approx \frac{2sin[k(x-x')]}{x-x'}
    [/tex]

    He then substituted x' with the deBroglie wave length at the Fermi level. I'm not sure what the physical meaning is...
     
    Last edited: Apr 19, 2010
  2. jcsd
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