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1925: the first papers on quantum mechanics

Alexander S. Blum

Published Jan 1, 2025• 0 citations
Publisher

Abstract

A review of the foundational papers on matrix mechanics of Werner Heisenberg, Max Born, Pascual Jordan and Paul Dirac, which were written 100 years ago in the summer and fall of 1925.
DOI
10.1051/epn/2025208

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Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this paper, we shall discuss some new perspectives on (i) what could be the guiding intuitions for his discoveries and (ii) the origin of the Born-Jordan-Heisenberg canonical quantization rule. From this vantage point we may get an insight into Einstein's Quantum Riddle (Lande1974,Sommerfeld1918,Born1926) and a possible glimpse of what might come next after the last 100 years of Heisenberg's quantum mechanics.
This article discusses the history of quantum physics, beginning with an analysis of the process through which a community of quantum theorists and experimentalists came into being. In particular, it traces the roots and fruits of Max Planck’s papers in irreversible processes in nature. It proceeds by exploring the origin and subsequent development of Niels Bohr’s so-called ‘planetary model’ of the atom, focusing on the extension of the model by Arnold Sommerfeld and members of his school as well to Bohr’s use of his principles of correspondence and adiabatic invariance. It also considers the post-war years, as the problems of atomic spectroscopy sparked the development of new methodological approaches to quantum theory. Finally, it offers a history of the two distinct new forms of quantum mechanics put forward in the mid-1920s: Werner Heisenberg, Max Born, and Pascual Jordan’s matrix mechanics, and Erwin Schrödinger’s wave mechanics.
Abstract Driven by the idea that a physical theory should only deal with observable quantities, Werner Heisenberg, a young post-doc working with Max Born in Göttingen, who had earlier done his Ph.D. work under Sommerfeld in Munich, was led to introduce a new type of object which represented the transitions between Bohr-Sommerfeld orbits. Max Born realized and recognized these objects as matrices. Together with Pascual Jordan, another post-doc, they worked out a complete theory, matrix mechanics. They completed this work in a few months. We discuss the role of matrix mechanics in the development of quantum mechanics.
As mentioned in Chapter 1 , the Heisenberg matrix mechanics provides one of the three main avenues to quantum mechanics. This approach to quantum mechanics was disclosed in three papers authored by Heisenberg (1925) , Born and Jordan (1925) , and Born et al. (1926) . An iconic result from the Heisenberg–Born–Jordan contribution was the commutation rule ( 14.1 ) p q − q p = h 2 π i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315216720/70121b16-f2c6-4331-b1ba-eecb806b93da/content/eq595.tif"/>