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Mean values & density matrix

  1. Nov 1, 2015 #1
    1. The problem statement, all variables and given/known data
    A system's state of spin 1/2 is represented at t=0 by C*exp[-a2(p-p0)2]*{{1,0},{0,1}} where the density matrix is represented in the base of eighenvalues of Sz and the spacial vector is represented in the continuum base of statesPx, Py, Pz.
    Find <X>, <Px> and <ΔX>, <ΔPx>

    2. Relevant equations
    PA, ρ=Tr(ρEA)=ΣWi<ψi|A|ψi>
    (ΔA)2=<A2>-<A>2
    3. The attempt at a solution
    To calculate <X> I change ψ(p) to ψ(x)=1/(π0.25*√aħ)*exp[-0.5*(x/aħ)-ix(p0/ħ)].
    Now I have to find ΣWi<ψi|X|ψi>. Here it is where I start getting lost; I think I have to integrate the spacial part of ψ multiplied by x between +- infinite.
    Can someone please tell me if I'm right?

    Thank you very much.
     
  2. jcsd
  3. Nov 6, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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