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Probability of finding a particle in a box

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider ψ (x) for a particle in a box:

    ψn(x) = (2/L)1/2sin(n∏x/L)

    Calculate the probability of finding the particle in the middle half of the box (i.e., L/4 ≤ x ≤ 3L/4). Also, using this solution show that as ''n'' goes to infinity you get the classical solution of 0.5.


    2. Relevant equations



    3. The attempt at a solution

    I integrated and figured out the probability for n=1,2,3. For n=1 I got 1/2 + 1/∏ which is about 0.818. For n = 1 I got 1/2 and for n=3, I got 0.430.

    I don't understand where the problem asks "Also, using this solution show that as ''n'' goes to infinity you get the classical solution of 0.5." From my calculations, as n goes to infinity, it does not approach a value of 0.5.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 11, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    It will help if you can evaluate the integral for a general (unspecified) values of n and then look at the result as n goes to infinity.

    From the 3 values you have obtained, you can't tell whether or not the probability is approaching any specific value as n gets large. (By the way, I agree with your answers for n = 1 and 2, but not for n = 3.)
     
  4. Feb 11, 2013 #3
    Drawing a picture of some of the solutions might give you some insight into what kind of answer you are looking for.
     
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