Theorem: int_R e^{-t^2/2} dt - sqrt(2 pi) = 0 (Gaussian Fourier-pair zero-omega)

Theorem (THz Gaussian Fourier-pair canonical): the Gaussian pulse E(t) = e^{-t²/2} has Fourier transform Ê(ω) = √(2π)·e^{-ω²/2} - the unique self-similar Fourier-pair. At ω = 0: Ê(0) = ∫_R e^{-t²/2} dt = √(2π) (Gauss's standard integral,…