which had been derived from the transition probability of a resonant state with known lifetime. The equation follows from that of a harmonic oscillator with damping, and a periodic force.
The Breit-Wigner distribution has also been widely used for describing the non-interfering cross-section of particle resonant states, the parameters E0 (= mass of the resonance) and (= width of the resonance) being determined from the observed data. Observed particle width distributions usually show an apparent FWHM larger than , being a convolution with a resolution function due to measurement uncertainties. and the lifetime of a resonant state are related to each other by Heisenberg's uncertainty principle ( ).
A normal (Gaussian) distribution decreases much faster in the tails than the Breit-Wigner curve. For a Gaussian, FWHM = 2.355 , [ here is the distribution's standard deviation]. The Gaussian in the graph above would be even more peaked at x = 0 if it were plotted with FWHM equal to 1 (as the Breit-Wigner curve).