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Particle in a box probability

  1. Jan 21, 2007 #1
    1. The problem statement, all variables and given/known data

    A particle is in a cubic box with infinitely hard walls whose edges have length L. The wave functions of the particle are given by

    [tex]\psi(x)=Asin\frac{n\pi(x)}{L}Asin\frac{n\pi(y)}{L}Asin\frac{n\pi(z)}{L}[/tex]

    a) Find the value of the normalization constant A.
    b) Find the probability that the particle will be found in the range



    2. Relevant equations

    in a)--- both questions, do i really need to do the triple integral?

    3. The attempt at a solution

    is this right? [tex]A=L/8[/tex]
     
    Last edited: Jan 21, 2007
  2. jcsd
  3. Jan 21, 2007 #2

    Meir Achuz

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    It should be A^2=L/8. You can use the fact that sin^2 averages to 1/2 to do the integral quickly.
    For any given range, you would have to do the integral over those limits.
     
  4. Jan 21, 2007 #3

    Gokul43201

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    Yes, you need to do the triple integral - but it's essentially only doing the same integral thrice. Your value for A is incorrect. Also, typically, one doesn't write the wavefunction with the normalization constant A^3 as you've written above. Are you sure that's how it is in the question given to you?
     
  5. Jan 21, 2007 #4

    Gokul43201

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    That doesn't look right. I think you may have inverted it...
     
  6. Jan 21, 2007 #5

    Meir Achuz

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    Sorry. It was all wrong. It should be A^2=8/L^3. I did it in my cubical head.
     
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