# A Lorentzian distribution

1. Apr 6, 2010

### Niles

1. The problem statement, all variables and given/known data
Hi

If I have a Lorentzian distribution given by

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

then is Γ the FWHM?

2. Apr 6, 2010

### vela

Staff Emeritus
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.

3. Apr 12, 2010

### Rajini

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

4. Apr 12, 2010

### Niles

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