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Homework Help: Probability of finding a particle given psi squared graph

  1. Apr 30, 2010 #1
    1. knight_Figure_39_13.jpg
    The figure shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 2.40×10−2-mm-wide strip at:

    I'm then asked the probability of finding a particle at various spots on the x-axis. We'll go with x = 0.0 here.




    2. P(x)*delta(x) = psi2*delta(x)



    3. The big triangle has area 0.5(2mm)(0.5) = 0.5mm2. I then integrated from -1.2*10-2 to +1.2*10-2 because that width is centered around the 0.0 point of interest. I then evaluated the solution, 0.5x, at the boundaries, obtaining an answer of 0.012... although I don't think I'm going about this quite right.
     
  2. jcsd
  3. Apr 30, 2010 #2
    I know that P will be psi(x) squared multiplied about the length L given in the problem. However, from the graph I can get the integral of psi squared, which is simply the area under the curve. How do I compute psi squared itself?
     
  4. Apr 30, 2010 #3
    I know this is probably simple but I just don't see it. I don't see how to get an equation that's a function of x that I can plug my x values into. For example, when it asks me for the probability at x=o over a length L, I know that the integral of psi squared is just (1/2)bh = 0.5, but it can't be that I just multiply that by L because the position x didn't play a role................
     
  5. Apr 30, 2010 #4
    Really lost here...

    I just tried solving it using a problem in my book as an analogy. For the probability at x = 0:

    I said that the equation describing one half of the "big triangle" is 0.50(1-x/1nm), which is psi squared. Solving with x = zero then multiplying by two to account for the otehr half of the triangle, I get 0.5*2 = 1, which I multiplied by 2.4*10^-2 = 0.024

    ???
     
  6. Apr 30, 2010 #5
    Nevermind got em
     
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