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Integration question re Fourier Transform

  1. Nov 30, 2004 #1
    Hello Listmembers,

    I am trying to make some progress in my understanding of
    Schrodinger's equation.I have been trying to teach myself about
    Fourier transforms in the hope that this will help me understand the
    derivation of Schrodinger's equation.

    My question has to do with slide number 16 from a presentation which can be found at :

    http://www.physics.gatech.edu/gcuo/UltrafastOptics/3803/OpticsI14FourierTransformI.ppt [Broken]

    My question is : I know about integrating the product of two
    functions [see Section 6.1 at
    http://mathews.ecs.fullerton.edu/c2002/ca0601.html] [Broken] but i don't see
    how you do end up with an expression containing "e" [i.e. the "exp"
    factor] by performing integrations on the fourier coefficients above
    it which contain sine and cosine functions ?

    Your help gratefully appreciated.
    Celal Berker
    London, England
    Last edited by a moderator: May 1, 2017
  2. jcsd
  3. Nov 30, 2004 #2
    Maybe I'm reading too quickly (or probably not at all), but that just looks like an application of the complex exponential.

    [tex]e^{-i \theta} = \cos{\theta} - i\sin{\theta}[/tex]

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