Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.
Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.
The report by Born and Heisenberg on ‘quantum mechanics’ may seem surprisingly difficult to the modern reader. This is partly because Born and Heisenberg are describing various stages of development of the theory that are quite different from today's quantum mechanics. Among these, it should be noted in particular that the theory developed by Heisenberg, Born and Jordan in the years 1925–6 and known today as matrix mechanics (Heisenberg 1925b [1], Born and Jordan 1925 [2], Born, Heisenberg and Jordan 1926 [4]) a differs from standard quantum mechanics in several important respects. At the same time, the interpretation of the theory (the topic of Section II of the report) also appears to have undergone important modifications, in particular regarding the notion of the state of a system. Initially, Born and Heisenberg insist on the notion that a system is always in a stationary state (performing quantum jumps between different stationary states). Then the notion of the wave function is introduced and related to probabilities for the stationary states. At a later stage, probabilistic notions (in particular, what one now calls transition probabilities) are extended to arbitrary observables, but it remains somewhat unclear whether the wave function itself should be regarded as a fundamental entity or merely as an effective one. This may reflect the different routes followed by Born and by Heisenberg in the development of their ideas. The common position presented by Born and Heisenberg emphasises the probabilistic aspect of the theory as fundamental, and the conclusion of the report expresses strong confidence in the resulting picture.
Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.
Abstract Quantum mechanics was developed to understand atomic structures. In 1925, Heisenberg introduced observables, which embodies the concept of quantum dynamical variables. Unlike classical variables, observables can be incompatible with each other. With Max Born, Paul Dirac, Pascual Jordan, and Wolfgang Pauli, they developed matrix mechanics. Six months later Schrodinger, working independently, launched wave mechanics. It introduced the wave function, which embodies the concept of quantum-mechanical states and the principle of superposition.
This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.
Abstract The celebrated three-men paper, which gave the first extensive account of the new quantum mechanics, started by Heisenberg in the summer of 1925, appeared in print in February 1926 (see Episode 37). On its first page it contains a note added in proof : ‘In a paper by P. Dirac [1] which has appeared in the meantime independently some of the results [in the Born–Jordan paper and in the three-men paper] and new conclusions drawn from the theory have been given.’ How did it happen that in the short time available an unknown outsider could have done independent and new work?
High Resolution Image Download MS PowerPoint Slide In July 1925, Werner Heisenberg submitted a paper to Zeitschrift für Physik entitled ‘On quantum-theoretical reinterpretation of kinematic and mechanical relationships’, thus giving birth to quantum mechanics. In the following year, building on de Broglie’s wave-particle duality, Erwin Schrödinger developed wave mechanics, and soon, Max Born provided a probabilistic interpretation of the wave function. The theory was further enriched by the exclusion principle of Wolfgang Pauli and the uncertainty principle of Heisenberg, which ultimately led to the development of relativistic quantum mechanics by Dirac. The Copenhagen Interpretation created a probabilistic framework for understanding the theory. Over the past century, quantum mechanics has paved the way for advances in quantum field theory, computing, and modern technologies. This historical narrative provides insights into the complex discovery process that led to the development of quantum mechanics, which can potentially guide novel breakthroughs amid challenging conceptual struggles, as seen in the field of artificial intelligence today.