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Student Support Forum: 'Fourier Transform of a Lorentz function' topicStudent Support Forum > General > "Fourier Transform of a Lorentz function"

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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: ,

Subject (listing for 'Fourier Transform of a Lorentz function')
Author Date Posted
Fourier Transform of a Lorentz function Pierre 09/09/12 4:25pm
Re: Fourier Transform of a Lorentz function Bill Simpson 09/09/12 9:22pm
Re: Re: Fourier Transform of a Lorentz function Pierre 09/10/12 1:33pm
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