OPERATOR CALCULUS. THE LOST FORMULATION OF QUANTUM MECHANICS

A review of the historical context of Born-Wiener’s contribution to the introduction of operational calculus in quantum mechanics.

In the early days of quantum mechanics, the problem of linear motion posed some difficulties for the development of the theory. In our talk we will argue that translating the theory from periodic to non-periodic motion required the improvement of the tools available to physicists and mathematicians. Mathematicians did not recognize as valid, at the time, the Fourier transforms of functions not complying with the usual requirements. As a background information we will also review the status of some mathematical instruments (Fourier analysis, Green kernels, Dirac’s delta functions…) needed to understand the challenges faced by Born and Wiener.

Graph appeared in: Gimeno, Gonzalo, Mercedes Xipell, and Marià Baig. 2021. "Operator Calculus. the Lost Formulation of Quantum Mechanics." Archive for History of Exact Sciences75 (3): 283-322.