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Cracker Jack
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Homework Statement
Given the following k-space representation of the wave function:
Ψ(k,t) = Ψ(k)e-iħk2t/2m
use the wave number representation to show the following:
<x>t=<x>0 + <p>0t/m
<p>t=<p>0
Homework Equations
<x>=∫Ψ*(x,t)xΨ(x,t)dx
<p>=∫Ψ*(x,t)(-iħ ∂/∂x)Ψ(x,t)dx
The Attempt at a Solution
I have tried to make the k-space representation into the normal Ψ(x,t) representation then taking Ψ*(x,t) and taking that integral where Ψ(x,t)=1/√(2pi)∫Ψ(k)e-iħk2t/2m*ei(kx-ħk2t/2m)dkHowever, I get caught up when calculating <x> at the following integral: <x>=1/2pi*∫∫(Ψ*(k)Ψ(k) x dk)dx