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. Thanks!