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 > >