# Particle Physics question.

1. Jan 16, 2014

### Tiberius47

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.
$\Gamma$=$\hbar$/$\tau$
Relativistic Breit-Wigner distribution
P_rel_=$\Gamma$/((E^2-M^2)^2+M^2$\Gamma$^2)
Wave function of particle at rest.
ψ(t)=ψ(0)e^(-iEt/$\hbar$)
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. Jan 16, 2014

### maajdl

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. Jan 16, 2014

### Tiberius47

Oh wow, duh. It's been over a year since I've taken quantum and I assumed the distribution would be relevant somehow.