# A Lorentzian distribution

## 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
Staff Emeritus
Homework Helper

## 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.

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.