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Normalization Question

  1. Mar 12, 2008 #1
    1. The problem statement, all variables and given/known data

    In a double-slit experiment, the slits are on the y-axis and the electrons are detected
    on a vertical screen. When only slit #1 is open, the amplitude of the wave which
    gets through is
    [tex] \psi(y,t) = A \exp^{-y^2} \exp^{-i((ky-\omega t)} [/tex]

    when only slit #2 is open, the amplitude of the wave which gets through is
    [tex] \psi(y,t) = A \exp^{-y^2} \exp^{-i(k+\pi)y-\omega t)} [/tex]

    (a) Normalize 1 and 2.


    2. Relevant equations

    Normalization Condition
    [tex] \int_{-\infty}^{\infty}\psi*\psi dy = 1 [/tex]

    3. The attempt at a solution


    1.
    [tex] 1=\int_{-\infty}^{\infty} A (\exp^{-y^2} \exp^{-i((ky-\omega t)}) (\exp^{-y^2} \exp^{i((ky-\omega t)}) dy
    [/tex]
    [tex]1=A \int_{-\infty}^{\infty} \exp^{-2y^2} dy
    [/tex]
    [tex]
    1/A= \sqrt{\pi/2}
    [/tex] From integral tables

    That's the solution i came up with for the first normalisation
    Is the second the same?
     
    Last edited: Mar 12, 2008
  2. jcsd
  3. Mar 12, 2008 #2
    i think u forgot to put the square over the A

    cioa
     
  4. Mar 13, 2008 #3
    Ha! So i did, thanks.
     
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