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A question about probabilities

  1. Sep 29, 2009 #1
    In need to know if my answer is correct. I tried to place this question on the homework forum but it seems that this kind of questions are not answered there.
    In a one-dimensional problem, consider a system o two particles with wave function [itex]\psi(x_1,x_2)[/itex] the distance X_1 - X_2 between, the two particles is measured. What is the probability of finding a result included between -d and +d
    My answer is :

    [tex]\int_{-\infty}^\infty dx_1 \int_{-d}^{+d}de |\psi(x_1,x_1-e)|^2 [/tex]

    I'd appreciate any comments!
     
  2. jcsd
  3. Sep 29, 2009 #2

    Fredrik

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    You should also explain how you got that result.
     
  4. Sep 29, 2009 #3
    I reason like this: d=x_2-x_1, x_2=d-x_1,the states that give the desired results are [itex]\{|x_1,d-x_1>,\quad -\infty<x_1<\infty\}[/itex]
    then mean value of the proyector on the eigen-subspace genarated by those kets[itex] P_n=\int_{-\infty}^\infty dx_1 |x_1,d-x_1><x_1,d-x_1| [/itex] should yield the answer
    [tex]<\psi|P_n|\psi>=\int_{-\infty}^\infty dx_1 |<x_1,d-x_1|\psi>|^2 \Delta d [/tex]
    for the probability of [itex]x_2-x_1[/itex] being between [itex]d \quad and \quad d +\Delta d[/itex]
     
  5. Oct 5, 2009 #4
    It seems correct to me although your explanation's first line is a little bit confuse.

    best regards

    DaTario
     
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