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Normalization Question

  • Thread starter Tyst
  • Start date
26
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1. Homework Statement

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. Homework 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:

Answers and Replies

173
0
1. Homework Statement

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. Homework 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?
i think u forgot to put the square over the A

cioa
 
26
0
Ha! So i did, thanks.
 

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