1. The problem statement, all variables and given/known data Knowing the momentum operator -iħd/dx , the expectation value of momentum and the Fourier transforms how can I prove that <p> = ∫dk [mod square of ψ(k)] h/λ. From this, mod square of ψ(k) is defined to be equal to P(k) right? 2. Relevant equations Momentum operator, p: -iħd/dx Expectation value of p: <p> = ∫ψ(x)*pψ(x)dx Fourier transform (not going to type here assuming it is known since it is a lengthy pair of eqs) 3. The attempt at a solution I have tried various "tactics" but the closest I got was through these steps. I used the fourier transforms of ψ(x) and ψ*(x) to get ψ(k) and ψ*(k) somewhere in the eq for <p>. I tried to integrate by parts to pull both ψ(k) out in front so it would form mod square ψ(k). Basically i get as constants ∫[h/(2piλ)][mod square of ψ(k)]*[a large integral]dk. Here is where i got stuck from the solution the integral should equal 2pi which it looks like it doesn't. Thank you for your time. This problem seems important to know but I just can't find any solutions online.