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Average velocity of free particle

  1. Sep 10, 2016 #1
    1. The problem statement, all variables and given/known data
    The wave function is given as Ψ(x,t) = Ae^[i(k1x-ω1t)] + Ae^[i(k2x-ω2t)].
    Show that particle average velocity Vav = ħ(k1+k2)/2m equals ω2-ω1/k2-k1.
    Average momentum of the particle is Pav = ħ(k2+k1)/2.

    2. Relevant equations
    p = ħk
    E=ħω
    K = 1/2 * mV^2

    3. The attempt at a solution
    if we calculate |Ψ(x,t)|^2 = 2*A(1+cos((k2-k1)x-(ω2-ω1)t)) form V=ω/k we get ω2-ω1/k2-k1.
    if we use average momentum Vav = Pav/m we get Vav = ħ(k1+k2)/2m.
    my problem is to get mathematically form ħ(k1+k2)/2m to ω2-ω1/k2-k1
     
  2. jcsd
  3. Sep 10, 2016 #2

    PeroK

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    What about using the relationship between energy and momentum?
     
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