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Uncertainty time/frequency

  1. Oct 27, 2011 #1
    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! ;-)
     
  2. jcsd
  3. Oct 27, 2011 #2

    Bill_K

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    Science Advisor

    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).
     
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