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Relationship between Group Velocity and Particle Velocity

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove that the group velocity of a wave packet is equal to the particle’s velocity
    for a relativistic free particle.


    2. Relevant equations

    vgroup = Δω/Δk = dω/dk
    E = (h/2π)*ω = √(p2c2 + m2c4)

    3. The attempt at a solution

    I'll be honest..I have no idea where to even begin with this problem.

    I know that vparticle = f*λ but I've got no idea how to begin besides that. If anyone could help with that it'd be great.

    Thanks!
     
  2. jcsd
  3. Feb 12, 2014 #2
    You must have seen what the wave packet solution is for a free particle, so start with that and see what ω is there and relate this to your first equation Δω/Δk.
    Do you obtain something familiar? (hint: in terms of momentum?)
     
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