# Who first noted the connection between Heisenberg's Uncertainty Principle and the Fourier Transform?

This is a question about the history of Quantum Mechanics. Who first noted the connection between Heisenberg's Uncertainty Principle and the Fourier Transform?

• Crossposted from physics.stackexchange.com/q/397631/2451 – Qmechanic Apr 4 '18 at 16:05
• Wikipedia says Kennard (1927, p. 339), Weyl (1928, p. 272). Weyl credits Pauli (see translation pp. 77, 393). – Francois Ziegler Apr 4 '18 at 16:11
• 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 4 '18 at 16:27
• Kennard 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 4 '18 at 17:02
• I've also found that the first person who actually mentions Fourier seems to be Darwin (1927, rspa.royalsocietypublishing.org/content/117/776/258) – Marc Apr 4 '18 at 19:04