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[Q] square of 'sinc function' integral

  1. Oct 15, 2008 #1

    I tried to solve some problem that i should get probability density with which eigenstate of

    momentum is chosen after momentum measurement by using [tex]<\varphi_{k}|\Psi>[/tex]

    I faced some stuck integral problem such as [itex]\int_{k_o}^0\frac{sin^{2}(2x)}{2x^{2}}dx[/itex]

    I transformed [itex]sin^{2}(2x) = \frac{1 - cos(2x)}{2}[/itex] so i obtained [itex]\int_{k_o}^0\frac{1-cos(2x)}{2x^{2}}dx[/itex] but i don't know next step because, [itex]\int_{k_o}^0\frac{1}{x^2}dx[/itex] go up to infinity,diverse.

    i tried to do partial integral such as [itex]\int udv = uv - \int vdu[/itex] but encountered same problem.

    How can i overcome this singular point problem? i convinced that [itex]\int_{k_o}^0\frac{sin^{2}(2x)}{2x^{2}}dx[/itex]

    should be solved to convegence because graphic of [itex]\frac{sin^{2}(2x)}{2x^{2}}[/itex].

    Please help me and give me an answer.
  2. jcsd
  3. Oct 15, 2008 #2
    i think you can try to write the cos as a series form.
    P.S. the third formular in your statements seems....
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