Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Cambridge University Press eBooks

THE ORIGIN AND DEVELOPMENT OF THE NEW QUANTUM MECHANICS

George Birtwistle

Published Jul 20, 2009• 0 citations
Publisher

Abstract

The origin of the new quantum mechanics was an epoch-making memoir by Werner Heisenberg which contained the new concept which was to lead to the phenomenal developments of quantum mechanics of the past two years. Up to this time the quantum theory (the ‘older’ quantum theory) postulated the existence of stationary states of the atom calculated by the use of the classical mechanics and selected by the use of quantum conditions satisfied by the action variables of that theory. In the new mechanics the equations have the same form as in the classical theory, but the variables no longer satisfy the commutative law of multiplication, that is, xy is not in general equal to yx ; the quantum conditions of the older theory are replaced by equations which enable the difference xy – yx to be calculated; these equations involve Planck's constant h. For some years before 1925, Sommerfeld, Heisenberg, Landé and Pauli had been grappling with the complex problem of the multiplets and their Zeeman separations. By the use of a system of quantum numbers l, s, j connected with the respective angular momenta of the series electron, the core, and the whole atom, they had given a qualitative account of the multiplets of the alkalis, alkaline earths, etc., the work culminating in a very general empirical formula—the g -formula of Landé—which enabled the Zeeman separations of a multiplet to be worked out quantitatively in terms of the quantum numbers l, s, j.

DOI
10.1017/cbo9780511694264.002

Related papers

The Historical and Physical Foundations of Quantum Mechanics

Robert Golub, S. K. Lamoreaux

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.

•Feb 28, 2023•10 citations

On the theory of quantum mechanics

P. A. M. Dirac

Abstract The new mechanics of the atom introduced by Heisenberg may be based on the assumption that the variables that describe a dynamical system do not obey the commutative law of multiplication, but satisfy instead certain quantum conditions. One can build up a theory without knowing anything about the dynamical variables except the algebraic laws that they are subject to, and can show that they may be represented by matrices whenever a set of uniformising variables for the dynamical system exists. It may be shown, however (see 3), that there is no set of uniformising variables for a system containing more than one electron, so that the theory cannot progress very far on these lines. A new development of the theory has recently been given by Schrödinger. Starting from the idea that an atomic system cannot be represented by a trajectory, i. e., by a point moving through the co-ordinate space, but must be represented by a wave in this space, Schrödinger obtains from a variation prin­ciple a differential equation which the wave function ψ must satisty. This differential equation turns out to be very closely connected with the Hamiltonian equation which specifies the system, namely, if H (qr, Pr - W = 0 is the Hamiltonian equation of the system, where the qr, Pr are canonical variables, then the wave equation for ψ is {H(qr, ih ∂/∂q) - W} ψ = 0.

Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character•Oct 1, 1926•1,041 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

THE BIRTH AND GROWTH OF QUANTUM THEORYFROM QUANTUM HYPOTHESIS TO QUANTUM MECHANICS

Peng Huan

This short history covers the birth and early growth of quantum theory from 1900 to 1928, beginning with Planck′s formula and the quantum hypothesis for the black-body radiation. After a description of the rise and decline of the old quantum theory in connection with its application in spectroscopy, two paths based on the rigorous formulation of the correspondence principle leading to matrix mechanics (1925) and Dirac′s non-commuting q-numbers (1925) are explained. Another path based on the generalization of the wave-particle aspect of lightquanta is then shown to lead to wave mechanics (1926). Among the works during the early growth of quantum mechanics in 1927—1928, representation theory, the uncertainty principle, two-electron problems, and Dirac′s relativistic theory of electrons are discussed.

•Jan 1, 2001•0 citations

The New Quantum Mechanics

George Birtwistle

George Birtwistle (1877–1929) published The New Quantum Mechanics in 1928. His stated aim was to give a detailed account of work which had brought the relatively new subject of quantum mechanics to the fore in the previous few years. The earlier chapters give a restatement of Alfred Landé's theory of multiplets which reconciles it with the new mechanics which follow. Later chapters present the matrix theory of Heisenberg, the q-number theory of Dirac and the wave mechanics of Schroedinger, and synthesise new theories, statistics and controversies in the work of de Broglie, Bose, Einstein, Fermi and Dirac. The book gives a complete overview of the state of quantum mechanics at the end of the second decade of the twentieth century, making it a valuable benchmark for historians of science and mathematicians alike.

Cambridge University Press eBooks•Jul 20, 2009•22 citations

The Postulates

M. Srirama Rao

In its beginning, quantum mechanics was approached in two completely different ways. Schrodinger, reasoning that electronic motions could be treated as waves, developed wave mechanics. The stationary states that an electron or molecule might have were analogues to standing waves set up by applying appropriate boundary conditions. Bohr’s theory could not explain the Stark and Zeeman effect, and the spectra of atoms more complex than alkali metals. In 1927, Heisenberg added one more dimension to the problem through the uncertainty principle. The postulates of any theory are a set of fundamental statements that are asked to be believed and draw conclusions from them. In classical mechanics, all dynamical variables are observables, but there are certain fundamental restrictions placed upon simultaneously measurable quantities in quantum mechanics.

CRC Press eBooks•Oct 13, 2022•0 citations
The origin of the new quantum mechanics was an epoch-making memoir by Werner Heisenberg which contained the new concept which was to lead to the phenomenal developments of quantum mechanics of the past two years. Up to this time the quantum theory (the ‘older’ quantum theory) postulated the existence of stationary states of the atom calculated by the use of the classical mechanics and selected by the use of quantum conditions satisfied by the action variables of that theory. In the new mechanics the equations have the same form as in the classical theory, but the variables no longer satisfy the commutative law of multiplication, that is, xy is not in general equal to yx ; the quantum conditions of the older theory are replaced by equations which enable the difference xy – yx to be calculated; these equations involve Planck's constant h. For some years before 1925, Sommerfeld, Heisenberg, Landé and Pauli had been grappling with the complex problem of the multiplets and their Zeeman separations. By the use of a system of quantum numbers l, s, j connected with the respective angular momenta of the series electron, the core, and the whole atom, they had given a qualitative account of the multiplets of the alkalis, alkaline earths, etc., the work culminating in a very general empirical formula—the g -formula of Landé—which enabled the Zeeman separations of a multiplet to be worked out quantitatively in terms of the quantum numbers l, s, j.
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.
Abstract The new mechanics of the atom introduced by Heisenberg may be based on the assumption that the variables that describe a dynamical system do not obey the commutative law of multiplication, but satisfy instead certain quantum conditions. One can build up a theory without knowing anything about the dynamical variables except the algebraic laws that they are subject to, and can show that they may be represented by matrices whenever a set of uniformising variables for the dynamical system exists. It may be shown, however (see 3), that there is no set of uniformising variables for a system containing more than one electron, so that the theory cannot progress very far on these lines. A new development of the theory has recently been given by Schrödinger. Starting from the idea that an atomic system cannot be represented by a trajectory, i. e., by a point moving through the co-ordinate space, but must be represented by a wave in this space, Schrödinger obtains from a variation prin­ciple a differential equation which the wave function ψ must satisty. This differential equation turns out to be very closely connected with the Hamiltonian equation which specifies the system, namely, if H (qr, Pr - W = 0 is the Hamiltonian equation of the system, where the qr, Pr are canonical variables, then the wave equation for ψ is {H(qr, ih ∂/∂q) - W} ψ = 0.
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 short history covers the birth and early growth of quantum theory from 1900 to 1928, beginning with Planck′s formula and the quantum hypothesis for the black-body radiation. After a description of the rise and decline of the old quantum theory in connection with its application in spectroscopy, two paths based on the rigorous formulation of the correspondence principle leading to matrix mechanics (1925) and Dirac′s non-commuting q-numbers (1925) are explained. Another path based on the generalization of the wave-particle aspect of lightquanta is then shown to lead to wave mechanics (1926). Among the works during the early growth of quantum mechanics in 1927—1928, representation theory, the uncertainty principle, two-electron problems, and Dirac′s relativistic theory of electrons are discussed.
George Birtwistle (1877–1929) published The New Quantum Mechanics in 1928. His stated aim was to give a detailed account of work which had brought the relatively new subject of quantum mechanics to the fore in the previous few years. The earlier chapters give a restatement of Alfred Landé's theory of multiplets which reconciles it with the new mechanics which follow. Later chapters present the matrix theory of Heisenberg, the q-number theory of Dirac and the wave mechanics of Schroedinger, and synthesise new theories, statistics and controversies in the work of de Broglie, Bose, Einstein, Fermi and Dirac. The book gives a complete overview of the state of quantum mechanics at the end of the second decade of the twentieth century, making it a valuable benchmark for historians of science and mathematicians alike.
In its beginning, quantum mechanics was approached in two completely different ways. Schrodinger, reasoning that electronic motions could be treated as waves, developed wave mechanics. The stationary states that an electron or molecule might have were analogues to standing waves set up by applying appropriate boundary conditions. Bohr’s theory could not explain the Stark and Zeeman effect, and the spectra of atoms more complex than alkali metals. In 1927, Heisenberg added one more dimension to the problem through the uncertainty principle. The postulates of any theory are a set of fundamental statements that are asked to be believed and draw conclusions from them. In classical mechanics, all dynamical variables are observables, but there are certain fundamental restrictions placed upon simultaneously measurable quantities in quantum mechanics.