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Probability to Find a Particle

  1. Apr 18, 2014 #1

    Nugso

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    1. The problem statement, all variables and given/known data

    Suppose we have a particle in 1-dimension, with wavefunction [tex]Ae^{-\frac{|x|}{2d}}[/tex] . What is the probability to find the particle in the interval [0,d]?
    Please provide your answer in terms of A, d, mathematical constants such as π (entered as pi) or e (entered as e). (Assume that A is real)



    2. Relevant equations

    [tex]∫ψ²dx = 1[/tex]




    3. The attempt at a solution

    I think I need to find A by normalizing it. [tex]∫ψ²dx = 1[/tex]

    By integrating it, I get [tex] A= 1/\sqrt{2d} [/tex]

    Now, I have to integrate it again, but this time with the interval of [0,d]

    [tex]∫1/sqrt(2d)*e^{-\frac{|x|}{2d}}*1/sqrt(2d)*e^{-\frac{|x|}{2d}}dx [/tex]

    and the answer I'm finding is, [tex]1/2*(1-e^{-1/d})*d[/tex]

    But somehow the answer is wrong. How do I correct it?
     
    Last edited: Apr 18, 2014
  2. jcsd
  3. Apr 18, 2014 #2
    I would check your solution for A again.
     
  4. Apr 18, 2014 #3

    Dick

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    Homework Helper

    Check it again. How did you wind up with a -1/d in the exponent?
     
  5. Apr 23, 2014 #4

    Nugso

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    Sorry for the late reply. I checked it and corrected the mistake.
     
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