Hi, I'm trying to derive a wave equation for a gaussian wavepacket for both the position (x) and the momentum (k), for a wave packet of width sigma, at some initial position x0 and with an initial momentum k0.(adsbygoogle = window.adsbygoogle || []).push({});

Now I have worked out the initial wavepacket equation to be:

psi(x) = (sigma*sqrt(pi))^1/2 * exp(-(x-x0)^2 / 2*sigma^2) * exp(ik0(x-x0)

and I've fourier transformed the result to get the initial momentum wavepacket:

phi(k) = (sigma/sqrt(pi))^1/2 * exp(-(sigma^2 * (k-k0)^2) / 2) * exp(-ik0x)

Now i'm not sure how to progess in order to achieve a time dependent version of the equation.... Ive tried a few methods but i'm not too sure.... Any help would be great!

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# Time Evolution of Gaussian Wave packets

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