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Problems of Atomic Dynamics

Max Born

Published Jan 1, 1960• 22 citations

Abstract

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.

Related papers

Problems of Atomic Dynamics

J S Briggs

Max Born London: MIT Press 1972 pp xiv + 200 price £1·40 (paper) This is a paperback edition, in the series History of Science and Technology by MIT Press, of Born's classic course of lectures delivered at MIT in the winter of 1925–6. The first 20 lectures, on the 'old' and 'new' quantum theory, are literally history in the making as the elements of the new quantum theory were being assembled even as the series of lectures progressed.

Physics Bulletin•Oct 1, 1972•22 citations

Matrix mechanics

Malcolm S. Longair

Born's reaction In his reminiscences, Born recounted his memories of these exciting days (Born, 1978): ‘Meanwhile Heisenberg pursued some work of his own, keeping its idea and purpose somewhat dark and mysterious. Towards the end of the summer semester, in the first days of July 1925, he came to me with a manuscript and asked me to read it and decide whether it was worth publishing … He added that though he had tried hard, he could not make any progress beyond the simple considerations contained in his paper, and he asked me to try myself, which I promised … His most audacious step consists in the suggestion of introducing the transition amplitudes of the coordinates q and momenta p in the formulae of mechanics … I was most impressed by Heisenberg's considerations, which were a great step forward in the programme which we had pursued … After having sent Heisenberg's paper to Zeitschrift für Physik for publication, I began to ponder about his symbolic multiplication, and was soon so involved in it that I thought the whole day and could hardly sleep at night. For there was something fundamental behind it … And one morning … I suddenly saw the light: Heisenberg's symbolic multiplication was nothing but matrix calculus, well known to me since my student days from the lectures of Rosanes at Breslau.’

Cambridge University Press eBooks•Jan 31, 2013•0 citations

Quantum Physics

Suman Seth

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.

Oxford University Press eBooks•Jul 6, 2017•3 citations

Atoms, Metaphors and Paradoxes

Sandro Petruccioli

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.

Cambridge University Press eBooks•Nov 18, 1993•40 citations

Lectures on Quantum Mechanics (nonlinear PDE point of view)

Alexander Komech

We expose the Schrödinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schrödinger, Pauli and Dirac equations, as well as for the Maxwell equations. We explain in detail all basic theoretical concepts. We explain all details of the calculations and mathematical tools: Lagrangian and Hamiltonian formalism for the systems with finite degree of freedom and for fields, Geometric Optics, the Hamilton-Jacobi equation and WKB approximation, Noether theory of invariants including the theorem on currents, four conservation laws (energy, momentum, angular momentum and charge), Lie algebra of angular momentum and spherical functions, scattering theory (limiting amplitude principle and limiting absorption principle), the Lienard-Wiechert formulas, Lorentz group and Lorentz formulas, Pauli theorem and relativistic covariance of the Dirac equation, etc. We give a detailed oveview of the conceptual development of the quantum mechanics, and expose main achievements of the ``old quantum mechanics'' in the form of exercises. One of our basic aim in writing this book, is an open and concrete discussion of the problem of a mathematical description of the following two fundamental quantum phenomena: i) Bohr's quantum transitions and ii) de Broglie's wave-particle duality. Both phenomena cannot be described by autonomous linear dynamical equations, and we give them a new mathematical treatment related with recent progress in the theory of global attractors of nonlinear hyperbolic PDEs.

arXiv:math-ph/0505059•May 21, 2005•5 citations

Constructing Quantum Mechanics Volume Two

Michel Janssen B, Anthony Duncan A

Abstract This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the twentieth century. It covers the period 1923–1927. It traces how the old quantum theory of Bohr and Sommerfeld gave way to the matrix mechanics of Heisenberg and others, and to the wave mechanics of Schrödinger. It then turns to the emergence of statistical transformation theory and the Hilbert space formalism unifying these two forms of the new quantum theory. It uses the metaphor of an arch built on a scaffold to capture these developments. The volume provides detailed analyses of the classic papers of Heisenberg, Born, Jordan, Pauli, Dirac, De Broglie, Einstein, Schrödinger, von Neumann, and others, which helped to lay the foundations of modern quantum mechanics. Drawing on correspondence and later reminiscences of these authors and synthesizing much of the extensive secondary literature on the breakthrough to modern quantum mechanics in the mid-1920s, this volume presents an authoritative new account of the genesis of quantum mechanics.

•Aug 17, 2023•49 citations

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.

Born's reaction In his reminiscences, Born recounted his memories of these exciting days (Born, 1978): ‘Meanwhile Heisenberg pursued some work of his own, keeping its idea and purpose somewhat dark and mysterious. Towards the end of the summer semester, in the first days of July 1925, he came to me with a manuscript and asked me to read it and decide whether it was worth publishing … He added that though he had tried hard, he could not make any progress beyond the simple considerations contained in his paper, and he asked me to try myself, which I promised … His most audacious step consists in the suggestion of introducing the transition amplitudes of the coordinates q and momenta p in the formulae of mechanics … I was most impressed by Heisenberg's considerations, which were a great step forward in the programme which we had pursued … After having sent Heisenberg's paper to Zeitschrift für Physik for publication, I began to ponder about his symbolic multiplication, and was soon so involved in it that I thought the whole day and could hardly sleep at night. For there was something fundamental behind it … And one morning … I suddenly saw the light: Heisenberg's symbolic multiplication was nothing but matrix calculus, well known to me since my student days from the lectures of Rosanes at Breslau.’

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.

This book gives a detailed study of the development and the interpretation given to Niels Bohr's Principle of Correspondence. It also describes the role that this principle played in guiding Bohr's research over the critical period from 1920 to 1927. Quantum mechanics, developed in the 1920s and 1930s by Bohr, Heisenberg, Born, Schrödinger and Dirac, represents one of the most profound turning points in science. This theory required a wholly new kind of physics in which many of the principles, concepts and models representing reality, that had formed the basis of classical physics since Galileo and Newton, had to be abandoned. This book re-examines the birth of quantum mechanics, in particular examining the development of crucial and original insights of Niels Bohr.

We expose the Schrödinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schrödinger, Pauli and Dirac equations, as well as for the Maxwell equations. We explain in detail all basic theoretical concepts. We explain all details of the calculations and mathematical tools: Lagrangian and Hamiltonian formalism for the systems with finite degree of freedom and for fields, Geometric Optics, the Hamilton-Jacobi equation and WKB approximation, Noether theory of invariants including the theorem on currents, four conservation laws (energy, momentum, angular momentum and charge), Lie algebra of angular momentum and spherical functions, scattering theory (limiting amplitude principle and limiting absorption principle), the Lienard-Wiechert formulas, Lorentz group and Lorentz formulas, Pauli theorem and relativistic covariance of the Dirac equation, etc. We give a detailed oveview of the conceptual development of the quantum mechanics, and expose main achievements of the ``old quantum mechanics'' in the form of exercises. One of our basic aim in writing this book, is an open and concrete discussion of the problem of a mathematical description of the following two fundamental quantum phenomena: i) Bohr's quantum transitions and ii) de Broglie's wave-particle duality. Both phenomena cannot be described by autonomous linear dynamical equations, and we give them a new mathematical treatment related with recent progress in the theory of global attractors of nonlinear hyperbolic PDEs.

Abstract This is the second of two volumes on the genesis of quantum mechanics in the first quarter of the twentieth century. It covers the period 1923–1927. It traces how the old quantum theory of Bohr and Sommerfeld gave way to the matrix mechanics of Heisenberg and others, and to the wave mechanics of Schrödinger. It then turns to the emergence of statistical transformation theory and the Hilbert space formalism unifying these two forms of the new quantum theory. It uses the metaphor of an arch built on a scaffold to capture these developments. The volume provides detailed analyses of the classic papers of Heisenberg, Born, Jordan, Pauli, Dirac, De Broglie, Einstein, Schrödinger, von Neumann, and others, which helped to lay the foundations of modern quantum mechanics. Drawing on correspondence and later reminiscences of these authors and synthesizing much of the extensive secondary literature on the breakthrough to modern quantum mechanics in the mid-1920s, this volume presents an authoritative new account of the genesis of quantum mechanics.