My teacher made up this question, but I think there's something wrong.
Consider the wave packet in momentum representation defined by Φ(p)=N if -P/2<p<P/2 and Φ(p)=0 at any other point. Determine Ψ(x) and uncertainties Δp and Δx.
Fourier trick and stuff...
The Attempt at a Solution
I found Ψ(x)=(2ħN/x√2πħ)sin(Px/2ħ), where N=±√1/P
<x>=0, <p>=0, <p^2>=(P^2)/12
But when I try to calculate <x^2>, I get a strange integral, which goes to infinity. Am I doing anything wrong?