Lorentzian Curve: Is It Normalized?

  • Thread starter Thread starter Sirben4
  • Start date Start date
  • Tags Tags
    Curve Lorentzian
Click For Summary
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.
Sirben4
Messages
3
Reaction score
0
Is a lorentzian curve by definition normalized? As far as I can tell it is such that ∫L(x) = 1.
 
Mathematics news on Phys.org
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Do existing EFE solutions support Closed Timelike Curves?
  • · Replies 7 ·
Replies
7
Views
738
Python How to properly normalize convolution of Gaussian and Lorentzian
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What kind of topology change does this Lorentzian metric describe?
  • · Replies 5 ·
Replies
5
Views
968
High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
MHB -7.64 Determine the following standard normal (z) curve areas:
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Degrees of Freedom in Lagrangian Mechanics for a Fractal Path
  • · Replies 2 ·
Replies
2
Views
1K
Confused by Lorentz transformation equation
  • · Replies 36 ·
2
Replies
36
Views
3K
Undergrad Off resonance driving of a MW/RF cavity
  • · Replies 9 ·
Replies
9
Views
624
High School Calculate distance between ends of a circle segment
  • · Replies 22 ·
Replies
22
Views
3K