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Finding the probability to find a particle in a well

  1. Nov 8, 2016 #1
    1. The problem statement, all variables and given/known data

    A particle is in the n = 1 state of an infinite square well of size L. T. What is the probability to find the particle in the region Δx = 0.007L at the point x = L/2? 3L/4? (Since Δx is small you don't need to do any integration)
    2. Relevant equations
    ψ = Δxf(x)
    Δx = 0.007L
    f(x) = sin2(nπx/L)

    3. The attempt at a solution
    I don't understand what I'm doing wrong. I can do the integral but I can't do this without doing the integral. I plugged in L/2 for Δx and x = L/2 for f(x) = sin2(nπx/L). This gave me the correct answer for L/2. But now I am trying to do 3L/4 and when I use the same method I get the wrong answer. I know the RIGHT answer is 0.007 for 3L/4 because of the nature of sine and a drawing of the wave-function in the well. I need to know how to properly do this mathematically- what am I doing wrong here?
     
  2. jcsd
  3. Nov 8, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Can you show more detail of your work for x = 3L/4? Make sure that you are using the normalized wavefunction for the ground state.
     
  4. Nov 9, 2016 #3
    I've figured it out - thank you
     
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