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Homework Help: Finding the probability density of a recombined beam.

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data
    So a neutron beam is split into two components, one by reflection, the other by transmission. The phase shift undergone by the reflected beam is [itex]\pi[/itex] radians, and the phase shift of the transmitted beam is [itex]\Delta[/itex].

    What is the equation of the probability density of the recombined wave?
    2. Relevant equations
    Wave equation psi = A*e^(i(kx - wt))

    3. The attempt at a solution
    I'm assuming that the expressions for the reflected wave is psi_r = psi * e^i*pi and the transmitted wave is psi_t = psi * e^i*del

    Then it would just be a simple case of adding them, and squaring the absolute of the sum to find the probability density? Which seems to be a simple algebra problem. But I can't for the life of me seem to arrive at the correct expression, given to be:

    rho = 2|psi|^2 * sin(del/2)^2, where psi is the equation of the original beam.

    A point in the right direction would be great, even if it's just affirming that my expressions for the reflected and transmitted waves are correct.

  2. jcsd
  3. Apr 6, 2013 #2


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    Homework Helper

    I think you've got it almost right. But does it make sense that the 'magnitudes' of the transmitted and reflected waves are each as great as the incoming wave?
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