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Normalizing a wavefunction

  1. Jan 30, 2016 #1
    1. The problem statement, all variables and given/known data
    the wavefunction upload_2016-1-30_13-3-48.png

    where < upload_2016-1-30_13-0-34.png | upload_2016-1-30_13-1-16.png > = upload_2016-1-30_13-0-5.png


    . I want to normalize it and find constant normalization A. A is real number.



    2. Relevant equations


    3. The attempt at a solution
    I know that for normalizing the wave function

    upload_2016-1-30_13-6-58.png
    but what happen for sigma? can I remove it from equation?
     

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  2. jcsd
  3. Jan 30, 2016 #2

    PeroK

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    You can't just ignore the sigma! First, can you find an expression for ##||\phi||^2##?
     
  4. Jan 30, 2016 #3
    I think the equation is :


    upload_2016-1-30_13-49-39.png


    because < upload_2016-1-30_13-0-34-png.png | upload_2016-1-30_13-1-16-png.png > = upload_2016-1-30_13-0-5-png.png is it correct? i'm not sure!
    but what I do after that?
     

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  5. Jan 30, 2016 #4

    PeroK

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    That's obviously not right. If you're stuck with an infinite sum, try a simple sum and see what happens. Try:
    ##\phi = A(\phi_0 + \frac{\phi_1}{3^4})##
     
  6. Jan 30, 2016 #5
    upload_2016-1-30_14-35-2.png and


    upload_2016-1-30_14-40-12.png for n = 0,1
    = A^2(1+1/3^8 + 1/5^8 + 1/7^8 + ... )
    then it is true that = A^2(1/(2n+1)^8) isn't it?
     

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  7. Jan 30, 2016 #6

    PeroK

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    Was that integral sign in post #3 a typo?

    For the next bit, trying googling "sums of reciprocal powers".
     
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