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Probability for particle in infinite square well

  1. Sep 16, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle is confined between rigid walls separated by a distance L=0.189. The particle is in the second excited state (n=3). Evaluate the probability to find the particle in an interval of width 1.00 pm located at
    a)x=0.188nm
    b)x=0.031nm
    c)x=0.79nm
    What would be the corresponding results for a classical particle


    2. Relevant equations
    P(X)=abs(ψ(x)^2)dx
    ψ(x)=(√2/L)*(sin(nπx/L)

    3. The attempt at a solution
    for part a
    P(x)=(2/.189)*(sin(3π(.0188))/.189))^2=.28/m

    I know the probability is just a matter of squaring ψ but my answer is way off. The got 2.63*10^-5 for part A. My first through was why does my answer have units of 1/m. I'm guessing i should multiply by dx. I thought this may be 1.00 pm but simply multiplying my answer by 10^-12 wont get the job done. Am i getting some variables mixed up here?
     
  2. jcsd
  3. Sep 16, 2015 #2
    What are the units of L? Are they in meters? Micrometers? Or even nanometers?

    That is what you have to find out!
     
  4. Sep 16, 2015 #3
    oh its L=0.189nm
     
  5. Sep 16, 2015 #4
    Does that fix your problem?

    When I figured it out (trial and error) I immediately got the right answer.
     
  6. Sep 16, 2015 #5
    Silly me i kept my calculator in radians instead of degrees. But anouther not is that the dx is actually something you need to multipy by, not just some kind of notation. was getting 2.6*10-2 until i realized i needed to multiply by 10^-12 m. thanks for the help
     
  7. Sep 17, 2015 #6
    Awesome.
     
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