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Particle Physics question.

  1. Jan 16, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that for real valued E a particle at rest can not decay.


    2. Relevant equations
    Width of resonance.
    [itex]\Gamma[/itex]=[itex]\hbar[/itex]/[itex]\tau[/itex]
    Relativistic Breit-Wigner distribution
    P_rel_=[itex]\Gamma[/itex]/((E^2-M^2)^2+M^2[itex]\Gamma[/itex]^2)
    Wave function of particle at rest.
    ψ(t)=ψ(0)e^(-iEt/[itex]\hbar[/itex])
    3. The attempt at a solution
    I guess Lambda would be 0 if tau (the lifetime of the particle) were infinite but I have no idea what that has to do with real valued E.
     
  2. jcsd
  3. Jan 16, 2014 #2

    maajdl

    User Avatar
    Gold Member

    Put a imaginary part on E and see the effect on |ψ|² and the total ∫|ψ|²dx .
    That's just a simple model to represent the decay of a particle.
    The total probability of presence would decay.
     
  4. Jan 16, 2014 #3
    Oh wow, duh. It's been over a year since I've taken quantum and I assumed the distribution would be relevant somehow.
     
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