How to Calculate Momentum Probability in an Infinite Well?

[greisen]

Hey all,

I am computing the probability that a particle in an infinite well has the momentum P in the ground state(0,a). So I start by calculating the wavefunction for the particle sqrt(2/a)*sin(pi*x). Than the probability can be calculated as
P(p) = |<p|psi>|^2. How to find <p| Fourier transformation ??

Any help appreciated

Thanks in advance

 

[dicerandom]

Your expression for the expectation value of the momentum isn't quite correct. Assuming that the boundaries of the well are at x=0 and x=a:

P(p) = < \psi | p | \psi > = \int_0^a \psi^* p \psi dx

Your expression for the wave function is a bit off as well. Recall that the wave function must be zero at the walls of the well.

(Sorry about the formatting, my LaTeX was throwing errors and it's too late for me to try and fix it )