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Relativistic Group Velocity

  1. Sep 29, 2007 #1
    1. The problem statement, all variables and given/known data

    "Use relativistic expressions for total energy and momentum to verify that the group velocity vg of a matter wave equals the velocity v of the associated particle."


    2. Relevant equations

    E[tex]^{2}[/tex] = (pc)[tex]^{2}[/tex] + (mc[tex]^{2}[/tex])[tex]^{2}[/tex]

    p = hbar * k

    E = hbar * [tex]\omega[/tex]

    vg = [tex]\frac{\partial \omega}{\partial k}[/tex]

    3. The attempt at a solution

    So I know how to do this, and I've seen the solution written out in many places (the Wikipedia article for 'group velocity', for example), but the final step of these derivations only works if the lorentz factor has a plus sign instead of a minus sign. My answer has a plus sign, and i'm not sure how i can justify writing it as the relativistic velocity... any ideas?
     
  2. jcsd
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