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Don'tKnowMuch
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Homework Statement
A particle is initially in the nth eigenstate of a box of length 2a. Suddenly the walls of the box are completely removed. Calculate the probability to find that the particle has momentum between p and p + dp. Is energy conserved?
Homework Equations
solution for particle in a box of length L ---->
ψ(x)(sub n) = (2/L)^1/2*sin(n∏x/L)
Fourier Transform of momentum space ----->
ζ(p) = [ 1/(2∏h-bar)^(1/2) ]*∫ e^(-ipx/h-bar)*ψ(x)
The Attempt at a Solution
I need the probability that the particle is between p & (p+dp). So my plan was to put the ψ(x)(sub n) into the Fourier transform, and then square that to get the probability. My trouble lies in the integral. I am not sure how to compute it. Would the bounds of the integral be p to (p+dp)?