| Author |
Comment/Response |
Pierre
|
 09/09/12 4:25pm
Hi
I'm surprised Mathematic does not give the correct Fourier Transform of a basic Lorentzian function:
Boltz = 1/(1 + x^2)
Transf_Boltz = FourierTransform[Boltz, x, X]
=> gives:
Exp(-Abs[X]) * Sqrt(Pi/2)
When normally it should give:
Exp(-Abs[X]) * Pi
Same story for a more complicated Lorentzian function:
Boltz_2 = 1/(1 + 4*x^2)
Transf_Boltz_2 = FourierTransform[Boltz_2, x, X]
=> gives:
(1/2) * Exp(-Abs[X]/2) * Sqrt(Pi/2)
When normally it should give:
Exp(-Pi*Abs[X]) * (Pi/2)
And when adding the width (Deltax or Dx) of the lorentzian function:
Boltz_3 = 1/(1+(2*(x-xo)/Dx)^2)
Then Mathematica gives even more funny things...
Can someone help ?
Attachment: Essai_11.nb, URL: , |
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