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.
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.
In 1925-26, the late Max Born gave two sets of lectures at M.I.T., one on the structure of the atom, the other on the lattice theory of rigid bodies. Problems of Atomic Dynamics contains the text of both sets.What gives this volume its remarkable interest is just those dates: 1925-26. This must have been, by all accounts, the headiest period in twentieth-century physics, and Max Born was one of the leaders of the ferment. As Norbert Wiener remembers, When Professor Born came to the United States [for these lectures in 1925] he was enormously excited about the basis Heisenberg had just given for the quantum theory of the atom.These lectures represent perhaps the most vivid written record of the transition between the old quantum theory of Bohr, and the new theory. At the time I began this course of lectures, Born writes, first paper on the quantum theory had just appeared. Here his masterly treatment gave the quantum theory an entirely turn. The paper of Jordan and myself, in which we recognized the matrix calculus as the proper formulation of Heisenberg's ideas, was in press, and the manuscript of a third paper by the three of us was almost completed.Even as the lecture series progressed, Born became familiar with results, which he introduced into his presentation: Pauli's fourth quantum number, Dirac's formalism, his own work on a general operational calculus. And yet, in spite of the conditions of revolutionary changes in physics that year -- in which established ancien regime principles were collapsing almost monthly -- the theory is developed with a cool elegance and with a formal completeness which may be regarded as a limiting case of its current state. These lectures represent the foundations of quantum theory, and they have withstood the tests of time -- the tests of more than forty years of experimental evidence.
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.