1. Oct 27, 2011 #1

   Gavroy

   

   hi
   
   i am looking for the correct equation, that gives me the linewidth by knowing the time of the emission process.
   
   so far, i found in the internet:
   
   Δf=1/(Δt), Δf=1/(4πΔt) and Δf=1/(2Δt)
   
   can you tell me, when i have to use which of these equations and maybe whether you think that these equations are correct?
   
   sry for my english, still practising! ;-)

    

   Gavroy, Oct 27, 2011
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3. Oct 27, 2011 #2

   Bill_K

   

   Science Advisor

   Insights Author

   Gavroy, Getting the factor right requires saying precisely what you mean by the lifetime and the linewidth. A decaying state is described by a wavefunction |ψ|² ~ exp(-Γt/ħ), so the lifetime of the state may be defined as Δτ = ħ/Γ.
   
   The shape of the line is a Lorentzian, 1/((E-E₀)² + (Γ/2)²) which reaches its half-height at E = E₀ ± Γ/2, so the "width" in that sense is ΔE = Γ. All right now ΔE = ħ Δω = 2π ħ Δf, so putting it all together you get Δf = 1/(2π Δτ).

    

   Bill_K, Oct 27, 2011

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