Lorentzian Curve: Is It Normalized?

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SUMMARY

A Lorentzian curve is defined as normalized when the integral of the function L(x) equals 1, specifically expressed as ∫L(x) dx = 1. The mathematical representation of the Lorentzian curve is given by L(x) = (1/π) * (1/(2Γ)) / ((x - x₀)² + (1/2Γ)²). This formulation confirms that the area under the curve integrates to 1, establishing its normalization.

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Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.
 
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Sirben4 said:
Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.
If we define it as [itex]L(x) = \frac{1}{\pi} \frac{\frac{1}{2} \Gamma}{(x-x_0)^2 + (\frac{1}{2} \Gamma)^2}[/itex], then [itex]\displaystyle \int_{-\infty}^{\infty} L(x) \ dx = 1[/itex].
 

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