Lorentzian Curve: Is It Normalized?

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A Lorentzian curve is defined such that its integral over all space equals one, indicating it is normalized. The specific form of the Lorentzian function is given by L(x) = (1/π) * (1/(2Γ)) / ((x - x0)² + (1/2Γ)²). This formulation confirms that the integral from negative to positive infinity results in a total area of one. Therefore, by definition, a Lorentzian curve is indeed normalized. The discussion clarifies the mathematical basis for this normalization property.
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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 L(x) = \frac{1}{\pi} \frac{\frac{1}{2} \Gamma}{(x-x_0)^2 + (\frac{1}{2} \Gamma)^2}, then \displaystyle \int_{-\infty}^{\infty} L(x) \ dx = 1.
 

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