Who first noted the connection between Heisenberg's uncertainty principle and the Fourier transform?
Who first noted the connection between Heisenberg's uncertainty principle and the Fourier transform?
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Crossposted from https://physics.stackexchange.com/q/397631/2451 – Qmechanic Apr 04 '18 at 16:05
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2Wikipedia says Kennard (1927, p. 339), Weyl (1928, p. 272). Weyl credits Pauli (see translation pp. 77, 393). – Francois Ziegler Apr 04 '18 at 16:11
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Wikipedia says that Kennard and Weyl proved the formal uncertainty relation. Do their papers mention the Fourier transform? (I don't have access to them). Also maybe my understanding of the Fourier transform is a bit rusty but Weyl doesn't explicitly mention it in your source and I don't see factors of $exp(ipx)$. – Marc Apr 04 '18 at 16:27
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1Kennard has the Fourier transform as equation (26), the uncertainty relation as (27). See also Pauli (1933, pp. 101-102) ($\varphi$ there is the Fourier transform of $\psi$) or Folland-Sitaram (1997, p. 209). – Francois Ziegler Apr 04 '18 at 17:02
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1I've also found that the first person who actually mentions Fourier seems to be Darwin (1927, http://rspa.royalsocietypublishing.org/content/117/776/258) – Marc Apr 04 '18 at 19:04
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Darwin does the free Gaussian wave packet the "modern (undergraduate) way", explicitly, but as he says, he is formalizing standard lore, following Bohr. The statements on the variance of the normal distribution have been long-standing lore in statistics... little to do with physics. – Cosmas Zachos Mar 07 '21 at 15:36