What is the FWHM of a Lorentzian distribution?

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SUMMARY

The discussion clarifies that in a Lorentzian distribution defined by the function f(x) = Γ / (x² + Γ²), the parameter Γ represents the half width at half maximum (HWHM), not the full width at half maximum (FWHM). To determine the FWHM, one must set f(x) to half its maximum value and solve for x, resulting in a difference of 2Γ. Additionally, the height of the Lorentzian distribution is confirmed to be 1/Γ.

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  • Familiarity with the concept of full width at half maximum (FWHM)
  • Basic algebra for solving equations
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Niles
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Homework Statement


Hi

If I have a Lorentzian distribution given by

<br /> f(x) = \frac{\Gamma}{x^2+\Gamma^2},<br />

then is Γ the FWHM?
 
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Niles said:

Homework Statement


Hi

If I have a Lorentzian distribution given by

<br /> f(x) = \frac{\Gamma}{x^2+\Gamma^2},<br />

then is Γ the FWHM?
Not quite. Just set f(x) to half its maximum value and solve for x. You'll get two solutions. Their difference is the full width at half maximum.
 
Hi,
In your case \Gamma is half width at half maximum. And height of Lorentzian is 1/\Gamma Correct?
 
Yes, I agree - because I get 2Γ to be FWHM. And I also agree on the height.
 

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