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Quantum probabilities calculation

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data
    In a one-dimensional problem, consider a system of two particles with which is associated
    the wave function [itex]\psi(x_1,x_2)[/itex]
    a) Give the probability of finding at least one of the partichles between a and b
    b)Give the probability of finding one and only one particle between a and b



    2. Relevant equations



    3. The attempt at a solution
    a)
    [tex]\int_{-\infty}^\infty dx_2 \int_a^b dx_1 |\psi(x_1,x_2)|^2 + \int_a^b dx_2\left(\int_{-\infty}^a dx_1|\psi(x_1,x_2)|^2 +\int_b^\infty dx_1|\psi(x_1,x_2)|^2 } \right)[/tex]
    b)
    [tex] \int_a^b dx_1\left(\int_{-\infty}^a dx_2 |\psi(x_1,x_2)|^2 +\int_b^\infty dx_2 |\psi(x_1,x_2)|^2 } \right)+\int_a^b dx_2\left(\int_{-\infty}^a dx_1 |\psi(x_1,x_2)|^2 +\int_b^\infty dx_1 |\psi(x_1,x_2)|^2 } \right)[/tex]
    I need to know whether these answers are correct or incorrect and some indication in case they are incorrect
     
  2. jcsd
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