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Why does the momentum of a matter wave depend on the phase velocity?

  1. Dec 18, 2011 #1
    de Broglie relations say that E = hf and p = h/λ which implies E/p = λf = ω/κ = vp, or p = E/vp. It seems to me like the momentum of a particle described by a matter wave should relate to the group velocity not the phase velocity, because the group velocity is generally the actual velocity of the particle.
     
  2. jcsd
  3. Dec 18, 2011 #2

    Bill_K

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    They're all related. The phase velocity is E/p while the group velocity is dE/dp. For a particle of mass m, E = p2/2m. So for this case the phase velocity is p/2m and the group velocity is p/m. Looks like the group velocity is what you want to be the "actual" velocity v.
     
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