Operator calculus: the lost formulation of quantum mechanics

Abstract

Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener’s joint contribution to the topic is generally bypassed in historical accounts of quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener’s work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions.