EARLY STEPS TOWARDS A “QUANTUM LINEAR MOTION”

A review of Wiener’s paper on operational calculus and the Born-Wiener paper on linear motion.

Max Born and Norbert Wiener worked out in 1925 the essentials of what was going to be considered one of the formulations (later largely ignored) of quantum mechanics. Their aim was to apply the tools of quantum mechanics to a more general type of problems: those with continuous spectrum.

In this talk we will introduce a relevant work of Wiener on operational calculus and we will emphasise its pioneering character. A brief analysis of the paper of Born and Wiener on linear motion will follow. We will argue that the authors’ reluctance to accept certain Fourier transforms (later Dirac delta functions) as valid mathematical objects contributed to the misinterpretation of their paper.

As a help for discussion, we will also review some basic elements of the current theory of distributions connected with this problem.

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.