The meaning of matrix mechanics: quantum jumps, optical dispersion, and Werner Heisenberg’s 1925 work

Abstract

In this article, we discuss the first formulation of quantum mechanics, proposed by Werner Heisenberg in 1925 and later called matrix mechanics. We emphasize the conceptual aspects, articulating the transition from existing theories (in particular, the Bohr atom and the optical theory of dispersion) to Heisenberg’s work. We argue that the major innovation brought by Heisenberg was adapting the formalism recently developed for the theory of optical dispersion by him and Hendrik Kramers, applying it to an emission process. We discuss the matrix aspect of Heisenberg’s proposal, which was fully understood in 1925 by Max Born and Pascual Jordan. We also discuss how the so-called Heisenberg picture is present in matrix mechanics. Finally, we reflect on the relevance of Heisenberg’s work for the current teaching of quantum mechanics. In particular, we propose a didactic articulation between the theoretical project of the Bohr atom and Heisenberg’s 1925 work, thus motivating quantum mechanics directly from the quantum transitions of the Bohr atom.