What is the FWHM of a Lorentzian distribution?

[Niles]

Homework Statement

Hi

If I have a Lorentzian distribution given by

$$f(x) = \frac{\Gamma}{x^2+\Gamma^2},$$

then is Γ the FWHM?

 

[vela]

Homework Statement

Hi

If I have a Lorentzian distribution given by

$$f(x) = \frac{\Gamma}{x^2+\Gamma^2},$$

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.

 

[Rajini]

Hi,
In your case $$\Gamma$$ is half width at half maximum. And height of Lorentzian is $$1/\Gamma$$ Correct?

 

[Niles]

Yes, I agree - because I get 2Γ to be FWHM. And I also agree on the height.