Abstract This chapter discusses how the new quantum theory took care of some of the failures of the old quantum theory and how it put the old theory’s successes on a firmer basis. Examples in the former category are the new theory’s resolution of the problems the old theory ran into with the anomalous Zeeman effect and helium (giving the wrong value for its ground state energy and being unable to explain the spectroscopic divide between ortho- and parahelium). Examples in the latter category are the fine structure in hydrogen and the Stark effect. The chapter also discusses some examples of Kuhn losses, instances where the new theory (at least initially) could not account for phenomena explained by the old one.
Abstract This chapter discusses how the new quantum theory took care of some of the failures of the old quantum theory and how it put the old theory’s successes on a firmer basis. Examples in the former category are the new theory’s resolution of the problems the old theory ran into with the anomalous Zeeman effect and helium (giving the wrong value for its ground state energy and being unable to explain the spectroscopic divide between ortho- and parahelium). Examples in the latter category are the fine structure in hydrogen and the Stark effect. The chapter also discusses some examples of Kuhn losses, instances where the new theory (at least initially) could not account for phenomena explained by the old one.
Abstract We consider three topics which proved frustratingly resistant to the methods of the old quantum theory up to the point of emergence of the quantum mechanics of Heisenberg and collaborators in late 1925. First, the old theory could not account convincingly for the superfluity of stationary states implied by the existence of the complex multiplets seen in most atomic spectra. Second, the progressively more complicated theories proposed for explaining the splittings of lines in the anomalous Zeeman effect were found to lead inevitably to glaring inconsistencies with the assumed mechanical equations of motion. Finally, there was the problem of the dual spectrum of helium, and even more basically, of the ground state energy of helium, all calculations of which in terms of specified electron orbits gave incorrect results. We relate the tangled history of the efforts to provide a theoretical resolution of these problems within the old quantum theory.
Abstract This chapter gives a summary, as non-technical as possible, of the rest of the book. It thus gives a brief synopsis of the development of matrix mechanics, wave mechanics, and two formalisms, statistical transformation theory and the Hilbert space formalism, tying the two together. It describes how the book covers the transition from the old to two distinct forms of the new quantum theory, including Bohr’s (unsuccessful) attempts in the early 1920s to account for the periodicity of the table of elements, and the introduction of two ingredients the first of which was indispensable for this task: Pauli’s (1925b) exclusion principle and Uhlenbeck and Goudsmit’s (1925) electron spin. It revisits the successes and failures of the old quantum theory and shows how the new theory took care of the failures and put the successes on a more solid basis.
Abstract We provide an overview, as non‐technical as possible, of the contents of Vol. 1 of the book. Reflecting the structure of the volume, this overview consists of two parts. In the first part, we summarize the most important early contributions to quantum theory (covered in detail in Chs. 2–4). This part starts with Planck’s work on black‐body radiation culminating in the introduction of Planck’s constant in 1900. It then moves on to Einstein’s 1905 light‐quantum hypothesis, his theory of specific heats, and his formulas for energy and momentum fluctuations in black‐body radiation. After summarizing Bohr’s path to his quantum model of the atom, it concludes with Einstein’s 1916–17 radiation theory combining elements of Bohr’s model with his own light‐quantum hypothesis. In the second part we summarize our analysis of the old quantum theory (given in detail in Chs. 5–7). After a brief overview of the career of Sommerfeld, who together with Bohr took the lead in developing the old quantum theory, we review the three principles we have identified as the cornerstones of the theory (the quantization conditions, the adiabatic principle, and the correspondence principle). We then discuss three of the theory’s most notable successes (fine structure, Stark effect, X‐ray spectra) and, finally, three of its most notorious failures (multiplets, Zeeman effect, helium).
Abstract This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
The transition from the atomic core model to the electron's spin, the debate on the adequacy of semi-classical models, and the lack of an appropriate scientific terminology are symptomatic of the revolutionary transition from the old quantum theory to the new quantum theory around 1921–5. As such, they provide us with a foil for rethinking Kuhn's view on scientific revolutions. In this view, scientific revolutions are distinctively accompanied by incommensurability between paradigms, or – to use Kuhn's later terminology – untranslatability between scientific lexicons. In the light of the historical reconstruction offered in Chapter 2, I shall here argue for the prospective intelligibility of the revolutionary transition around 1924 via a two-step argument that (1) reconsiders Kuhn's notion of incommensurability as untranslatability (Section 3.2), and (2) offers a positive account of the way the electron's Zweideutigkeit and the exclusion rule came out of the old quantum theory (Section 3.3). The revolutionary transition from the old quantum theory to the new quantum theory On 5 November 1980, Thomas Kuhn delivered a lecture at Harvard University entitled ‘The crisis of the old quantum theory: 1922–25’. In his distinctive style of reasoning, Kuhn presented the rise of quantum mechanics after 1925 as the result of a period of crisis of the old quantum theory between 1922 and 1925. The old quantum theory – in Kuhn's view – cannot be regarded as a full-blown theory but rather as a set of algorithms to solve problems and paradoxes.