Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contributors. The fundamental laws of Quantum Theory derived by Max Born and Pascual Jordan may mathematically be represented in many different ways, and particular emphasis is given to the distinction between physical content and mathematical representation.
Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contributors. The fundamental laws of Quantum Theory derived by Max Born and Pascual Jordan may mathematically be represented in many different ways, and particular emphasis is given to the distinction between physical content and mathematical representation.
The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.
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.
A hundred years ago, physics underwent one of its most dramatic transformations - a paradigm shift that fundamentally changed our understanding of nature. Over the course of several revolutionary months in 1925 and early 1926, quantum mechanics emerged as a new, foundational theory of the microscopic world. With the publication of key papers by Werner Heisenberg and Erwin Schrödinger, the theoretical framework was established that radically redefined our perception of physical reality. These works demonstrated that atoms and subatomic particles do not obey the laws of classical mechanics, but instead follow entirely new, quantum laws. Born in those intense months, quantum mechanics became one of the cornerstones of modern physics and a lasting source of inspiration in both theoretical and applied sciences. This paradigmatic shift opened new avenues of research and laid the groundwork for scientific discoveries that continue to shape our understanding of nature today. This paper is dedicated to those pivotal historical moments - the months in which science made one of its deepest leaps and most consequential strides in comprehending the world.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.
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.
The origin of the relativity theories was closely bound up with the development of electromagnetic concepts, a development that approached a coherent field-theoretical formulation, according to which all actions may vary in a continuous manner. In contrast, quantum theory arose out of the development of atomic concepts, a development that was characterized by the acknowledgment of a fundamental limitation to classical physical ideas when applied to atomic phenomena. This restriction was expressed in the so-called quantum postulate, which attributed to any atomic process an essential discontinuity that was symbolized by Planck’s quantum of action and soon incarnated in quantization condition (commutation or anticommutation relations) and uncertainty relations.