Why can't a particle at rest decay when its energy is real-valued?

In summary, the conversation discussed the proof that a particle at rest cannot decay for real values of energy (E). This was shown using the width of resonance (Γ), the relativistic Breit-Wigner distribution (P_rel_), and the wave function of a particle at rest (ψ(t)). The conversation also mentioned the effect of adding an imaginary part to E on the probability of presence, showing that the decay of a particle is represented by a simple model.
  • #1
Tiberius47
5
0

Homework Statement


Show that for real valued E a particle at rest can not decay.


Homework 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])

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.
 
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  • #2
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.
 
  • #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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