Abstract The thirteenth edition of the Encyclopaedia Britannica, published in 1926, contains three supplementary volumes ‘covering recent years’. These include an entry ‘Atom’ written by Bohr, dealing largely with the theory of the periodic system, actually a rather primitive version that did not yet include spin. Bohr also mentioned briefly a new theory dating from July 1925, Heisenberg’s quantum mechanics, ‘which constitutes a bold departure from the classical way of describing natural phenomena ⃛It has in particular allowed the Balmer formula to be derived.’ In his contribution Bohr continued to treat atoms with more than one electron in terms of the old quantum theory, however, since ‘the methods of quantum mechanics have not yet been applied to [this] problem’. Another entry, by Charles Barkla, also refers to quantum mechanics: ‘A new theory ⃛ has been formulated by Heisenberg which, whether fruitful or not, promises to put quantum mechanics in much more logical form. Its physical significance, however, is not apparent.’
Abstract The thirteenth edition of the Encyclopaedia Britannica, published in 1926, contains three supplementary volumes ‘covering recent years’. These include an entry ‘Atom’ written by Bohr, dealing largely with the theory of the periodic system, actually a rather primitive version that did not yet include spin. Bohr also mentioned briefly a new theory dating from July 1925, Heisenberg’s quantum mechanics, ‘which constitutes a bold departure from the classical way of describing natural phenomena ⃛It has in particular allowed the Balmer formula to be derived.’ In his contribution Bohr continued to treat atoms with more than one electron in terms of the old quantum theory, however, since ‘the methods of quantum mechanics have not yet been applied to [this] problem’. Another entry, by Charles Barkla, also refers to quantum mechanics: ‘A new theory ⃛ has been formulated by Heisenberg which, whether fruitful or not, promises to put quantum mechanics in much more logical form. Its physical significance, however, is not apparent.’
Abstract Following the path by which humanity learned quantum mechanics can lead to an improved understanding of the theory and the origins of its perceived limitations. Our goal is to retrace the development by investigating primary sources, including original published papers and letters, with attention to their timing and influence. Quantum mechanics began in 1900 with the introduction of Planck’s constant, which lead to the “old” quantum theory and Bohr’s model of the atom. With the introduction of matter waves in 1924, a second more intense period began. By 1928 the complete fundamental structure of quantum mechanics was established with the introduction of the Schrödinger equation, the proof of its equivalence to Heisenberg’s matrix mechanics, and the introduction of the relativistic Dirac equation. The theory retains the same essential form today, fueling the technological revolution that began in the last century. We culminate with an introduction to quantum information and computing. This completely new physical scientific paradigm was developed largely in Germany during a period of enormous social, economic, and political upheaval—in a hostile intellectual environment—that parallels the overturning of classical physics. It is striking that all the problems debated today were immediately recognized by the founders of the theory and instructive to see how they dealt with the various issues. We emphasize the centrality of the often neglected second quantization form of the theory for questions of interpretation and give a detailed examination of von Neumann’s widely misunderstood hidden variable theorem.
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.
Elements of quantum mechanics Quantum mechanics was discovered in 1925 through groping efforts to compromise two apparently contradictory pictures on the fundamental entities in nature. One was the wave picture for light which was later extended to matter by de Broglie, another was the corpuscular picture of matter which was later extended to light by Einstein. Schrödinger's wave equation came as a natural development of the first stream, while Heisenberg's matrix mechanics was presented as a unique proposal from the second stream. In spite of completely different appearances, the two theories proved, within a couple of years after their discoveries, to be equivalent. This is a most beautiful example that the physical reality exists independent of the mathematical framework formulated for its description. In this chapter, we will give a very brief review of the principles of quantum mechanics, 1–3 mainly with the harmonic oscillator as a model system for the following reasons. The first is historical: the electromagnetic wave, whose interaction with matter is the subject of this book, is a harmonic oscillator, a system which was for the first time subject to “quantization”, thus opening a way to the discovery of quantum mechanics. The second is technical: the harmonic oscillator is one of very few examples of analytically soluble problems in quantum mechanics. The third is pedagogical: the harmonic oscillator is a system best suited for realization of the equivalence of the two different pictures mentioned above and hence for a deeper understanding of the principles of quantum mechanics.
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
‘The new wave mechanics gave rise to the hope that an account of atomic phenomena might be obtained which would not differ essentially from that afforded by the classical theories of electricity and magnetism. Unfortunately, Bohr's statement in the following communication of the principles underlying the description of atomic phenomena gives little, if any, encouragement in this direction.’ This comment is to be found in the brief note prefaced by the editors of the British journal Nature to Niels Bohr's paper ‘The Quantum Postulate and the Recent Development of Atomic Theory’ in the supplement of 14 April 1928. The article in question is the famous paper which first introduced and defined the concept of ‘complementarity’ and outlined the basic points of what was to become known as the Copenhagen interpretation of quantum mechanics. In the paper, Bohr returned to the arguments contained in the paper discussed at the International Congress of Physicists held at Como in September 1927 to mark the centenary of the death of Alessandro Volta and published in the proceedings of the same congress. It was probably his conviction that the new viewpoint adopted in the description of nature fully expressed the theoretical and cognitive content of quantum physics coupled with his enthusiasm at having achieved ‘after many years of struggling in the dark […] the fulfilment of the old hopes’ that induced him to give his work broader and more prestigious circulation.
Quantum theory has passed through three distinct stages during its evolution. The first is generally referred to as ‘old quantum theory’. During a period roughly between 1900 and 1925 Planck, Bohr and Einstein, among others, grappled with various experimental and theoretical crises by patching up classical mechanics with some new quantum ideas applied as band-aids. This is not to disparage the work; it was vitally important, and you can only do what is possible at the time. The quantum world is very different to the picture painted by classical physics. That being the case and given the extreme nature of some of these differences, we might question the wisdom of accepting the quantum view. Scientists can be quite disparaging about philosophy, sometimes while in the process of espousing, quite stridently, a philosophical position of their own. The chapter also presents an overview on the key concepts discussed in this book.