What is the FWHM of a Lorentzian distribution?

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Homework Help Overview

The discussion revolves around the properties of a Lorentzian distribution, specifically focusing on the relationship between the parameter Γ and the full width at half maximum (FWHM).

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore whether Γ represents the FWHM and discuss the method of setting the function to half its maximum to find the FWHM.

Discussion Status

Some participants have provided guidance on how to determine the FWHM and have reached a point of agreement regarding the relationship between Γ and the FWHM, though no formal consensus is established.

Contextual Notes

There is an ongoing discussion about the definitions and relationships of parameters within the context of the Lorentzian distribution, including assumptions about the height of the distribution.

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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