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

European Journal of Physics

The road to matrix mechanics: I. Classical interpretation of the anomalous optical dispersion

L. Crivellari

Published Jun 30, 2016• 0 citations
Publisher

Abstract

Abstract This paper is the first one of a series of two on the role of the optical dispersion in the historical development of early quantum mechanics. As preparation for the successive paper on Ladenburg’s development of the phenomenological theory of radiative transitions between the stationary states of an atom by Einstein, we present here the current theories on optical dispersion between the second half of the 19th century and the beginning of the 20th century.

DOI
10.1088/0143-0807/37/5/055404

Related papers

The road to matrix mechanics: II. Ladenburg’s quantum interpretation of optical dispersion

L. Crivellari

Abstract This paper reviews Ladenburg’s development of the phenomenological theory of radiative transitions between the stationary states of an atom put forward by Einstein in 1917. The historical background as well as the far reaching outcomes of his work are considered and discussed; among them the Kramers–Heisenberg quantum dispersion theory that paved the way to Heisenberg’s formulation of matrix mechanics and the quantum-mechanical calculation of the spectral line profiles.

European Journal of Physics•Jun 30, 2016•0 citations

Dispersion Theory in the Old Quantum Theory

Anthony Duncan A, Michel Janssen B

Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.

•Aug 17, 2023•0 citations

Quantum optics

Gennaro Auletta, Mauro Fortunato, Giorgio Parisi A

The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.

Cambridge University Press eBooks•Apr 16, 2009•0 citations

Traditions and Transformations in the History of Quantum Physics

Christoph Lehner (ed.), Jürgen Renn, Shaul Katzir (ed.)

More than a century after the beginning of the quantum revolution, historians continue to explore new facets in the history of quantum physics, and to re-examine some of its better-known aspects. The thirteen papers collected in this volume, by authors from five continents, present central trends in the current study of quantum physics within its theoretical, experimental, philosophical, technological and social contexts. They discuss developments from the late nineteenth to the early twenty-first century and go beyond the traditional focus on Europe and North America to include China and Japan, and beyond the Heisenbergs and Diracs to reveal the role of actors who hitherto have played only a marginal role in historical account, but left their mark on the development of quantum physics. Also a wider array of subdisciplines comes into view, from optics to quantum gravity through quantum electrodynamics, from atomic and nuclear to condense matter physics and foundations of physics. Moreover, the volume shows that fields such as dispersion, physical chemistry and solid state physics should not be seen merely as areas of applications of ideas that evolved in other contexts, but should be regarded as birthplaces of important theoretical insights. The perspective of the papers ranges from local histories to global discussions, from conceptual changes via the role of experimentation to interactions with social and technological forces and to the interpretation of the theory.

•Jun 28, 2010•29 citations

Interpretation of quantum mechanics from the dynamics of ideal measurement

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

This year we celebrate the centennial of quantum mechanics, its incubation as wave mechanics by de Broglie and Schrödinger, and as matrix mechanics by Heisenberg, Born and Jordan. Its great potential has transformed the world forever, most notably through two quantum revolutions, the first one in the 20th century, and the second one emerging now.

Europhysics news•Jan 1, 2025•3 citations

Quantum Mechanics: Its Early Development And The Road To Entanglement And Beyond

Edward G. Steward

This book provides the reader with an explanation of the origin and establishment of quantum mechanics together with a descriptive survey of developments up to the present day. The mathematics is presented in a digestible form yet following the original approach. This second edition presents two new chapters to supplement and extend the first edition material. "Interpretations of Quantum Mechanics" surveys a wide range of current topics, including the multiverse, 't Hooft's ideas for a deterministic local field theory, a summary of the de Broglie-Bohm pilot-wave theory and Anthony Valentini's development of it, and speculative concluding comments on the way ahead.

•Oct 18, 2011•5 citations
Abstract This paper is the first one of a series of two on the role of the optical dispersion in the historical development of early quantum mechanics. As preparation for the successive paper on Ladenburg’s development of the phenomenological theory of radiative transitions between the stationary states of an atom by Einstein, we present here the current theories on optical dispersion between the second half of the 19th century and the beginning of the 20th century.
Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.
The behavior of light and its interaction with matter is certainly one of the most interesting phenomena of physics. It has puzzled thinkers and scientists in ancient Greece (Archimedes) and through the Middle Ages, at least since the times of Robert Grosseteste (1168–1235), right up to the theories of Galileo Galilei and Isaac Newton. The classical electromagnetic theory of light (see Tab. 13.1) was beautifully established in the second half of the nineteenth century with the Maxwell equations. Quantum optics is nothing other than the quantum theory of light. It finds its roots in Planck's discovery (1900) that the assumption of energy quantization for a harmonic oscillator allowed us to solve the black-body problem (see Subsec. 1.5.1). The successive early steps that led to the quantization of the electromagnetic field include Einstein's explanation of the photoelectric effect with the introduction of the quantum of light (see Subsec. 1.2.1) and the interpretation of atomic spectra (see Subsec. 1.5.4). Quantum optics is usually not covered by conventional textbooks on quantum mechanics. We include its discussion here for two main reasons: first, because it is a fundamental and advanced application of the basic framework of quantum mechanics, and, second, because in the last 30 years quantum optics has played (and is still playing) a major role in the advancement and understanding of quantum mechanics.
More than a century after the beginning of the quantum revolution, historians continue to explore new facets in the history of quantum physics, and to re-examine some of its better-known aspects. The thirteen papers collected in this volume, by authors from five continents, present central trends in the current study of quantum physics within its theoretical, experimental, philosophical, technological and social contexts. They discuss developments from the late nineteenth to the early twenty-first century and go beyond the traditional focus on Europe and North America to include China and Japan, and beyond the Heisenbergs and Diracs to reveal the role of actors who hitherto have played only a marginal role in historical account, but left their mark on the development of quantum physics. Also a wider array of subdisciplines comes into view, from optics to quantum gravity through quantum electrodynamics, from atomic and nuclear to condense matter physics and foundations of physics. Moreover, the volume shows that fields such as dispersion, physical chemistry and solid state physics should not be seen merely as areas of applications of ideas that evolved in other contexts, but should be regarded as birthplaces of important theoretical insights. The perspective of the papers ranges from local histories to global discussions, from conceptual changes via the role of experimentation to interactions with social and technological forces and to the interpretation of the theory.
This book provides the reader with an explanation of the origin and establishment of quantum mechanics together with a descriptive survey of developments up to the present day. The mathematics is presented in a digestible form yet following the original approach. This second edition presents two new chapters to supplement and extend the first edition material. "Interpretations of Quantum Mechanics" surveys a wide range of current topics, including the multiverse, 't Hooft's ideas for a deterministic local field theory, a summary of the de Broglie-Bohm pilot-wave theory and Anthony Valentini's development of it, and speculative concluding comments on the way ahead.