- #1
Niles
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Homework Statement
Hi
If I have a Lorentzian distribution given by
[tex]
f(x) = \frac{\Gamma}{x^2+\Gamma^2},
[/tex]
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.Niles said:Homework Statement
Hi
If I have a Lorentzian distribution given by
[tex]
f(x) = \frac{\Gamma}{x^2+\Gamma^2},
[/tex]
then is Γ the FWHM?
A Lorentzian distribution, also known as a Cauchy distribution, is a continuous probability distribution that describes the shape of a spectral line in physics and engineering. It is named after the Dutch mathematician Hendrik Lorentz.
A Lorentzian distribution is characterized by its long tails, which extend infinitely in both directions. It also has a single peak and is symmetric about its mean. Unlike a normal distribution, it does not have a finite variance or standard deviation.
A Lorentzian distribution differs from a normal distribution in several ways. While a normal distribution has a finite variance and standard deviation, a Lorentzian distribution has infinite variance and standard deviation. Additionally, the tails of a Lorentzian distribution extend infinitely in both directions, while the tails of a normal distribution decay rapidly.
The Lorentzian distribution is commonly used in physics and engineering to model spectral lines, such as in atomic and nuclear physics. It is also used in finance to model stock price fluctuations and in data analysis to fit data with long tails.
The Lorentzian distribution is not directly related to the Lorentz transformation in physics. However, both are named after the same mathematician, Hendrik Lorentz. The Lorentz transformation is a key concept in the theory of relativity, while the Lorentzian distribution is a probability distribution used in various fields of science.