Should we state it in the reverse? Like FT of a Gaussian has to be a Gaussian, and that's why the integral is a Gaussian.
The integral of a Gaussian times cosine is another Gaussian
This implies the Fourier Transform of a Gaussian is another Gaussian
In QM, this means that a free particle whose spectral function is a Gaussian is what's known as a "minimum uncertainty wave packet"pic.twitter.com/HQ1fa9ITAh
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you could state it in either direction.. by this implying the FT is a gaussian I just mean if you do the FT of a gaussian the i*sin(x) term vanishes and you're just left with this integral
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Dillion, do you believe this arise from the characteristics of a stable distribution?
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what do you mean by stable distribution?
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remind me with Eigens :)
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Wow. That's one I didn't know.
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