       Re: fourier transform

• To: mathgroup at smc.vnet.net
• Subject: [mg30316] Re: fourier transform
• From: "Kevin J. McCann" <kevinmccann at Home.com>
• Date: Sat, 11 Aug 2001 03:39:40 -0400 (EDT)
• References: <9kqjf4\$4do\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```There is an analytic answer I believe, but the brute force numerical
approach also works. I am sending you a nb on quantum mechanical gaussian
wave packets. Hope this helps.

Kevin

<c6wang at sciborg.uwaterloo.ca> wrote in message
news:9kqjf4\$4do\$1 at smc.vnet.net...
>
> Dear All,
>
> I am trying to work out a free space propagation of Gaussian beam. If I do
> not use any approximation, I am facing an Oscillating Fourier
> integration.  Could you offer me some suggestions?  Following is an
> example of my code:
>
> (*                ********************** *)
> a=1/.8; (* .8 is the wavelength *)
>
> dd =1000;  (* free space propagation distance is 1000 *)
>
> ff[x]=Exp[-x^2];   (* Gaussian beam *)
>
> FF[\[Omega]_]:=Sqrt[2 \[Pi] ]* FourierTransform [ff[x], x, \[Omega]];
>
> H[\[Omega]_]:=Exp[- I 2 \[Pi] * Sqrt[a^2 - \[Omega]^2]]  dd ;
>
>
> gg[X_]:=InverseFourierTransform[H[\[Omega]] FF[\[Omega]], \[Omega], X]
>
>
>
> (*                 ******                  *)
>
> Best Regards
>
>
> Connie Wang
>
>

```

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