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

Nonrelativistic Quantum Mechanics

Sunny Y. Auyang

Published Jul 27, 1995• 0 citations
Publisher

Abstract

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.

DOI
10.1093/oso/9780195093445.003.0002

Related papers

The invention of quantum mechanics—matrix mechanics

Robert Golub, S. K. Lamoreaux

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.

•Feb 28, 2023•0 citations

Fundamentals of Quantum Mechanics

Muhammad Suhail Zubairy

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.

Oxford University Press eBooks•May 7, 2020•6 citations

Creating Quantum Mechanics

Frank S. Levin

Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.

•Sep 21, 2017•0 citations

Quantum mechanics

Steven Weinberg

Our modern understanding of atoms, molecules, solids, atomic nuclei, and elementary particles is largely based on quantum mechanics. Quantum mechanics grew in the mid-1920s out of two independent developments: the matrix mechanics of Werner and the wave mechanics of Erwin Schrödinger. For the most part this chapter follows the path of wave mechanics, which is more convenient for all but the simplest calculations. The general principles of the wave mechanical formulation of quantum mechanics are laid out and provide a basis for the discussion of spin, identical particles. and scattering processes. The general principles are supplemented with the canonical formalism to work out the Schrödinger equation for charged particles in a general electromagnetic field. The chapter ends with the unification of the approaches of wave and matrix mechanics by Paul Dirac, and a modern approach, known as Hilbert space, is briefly described.

Cambridge University Press eBooks•Apr 21, 2021•0 citations

Enseignement

CERN

In an attempt to give an exact mathematical formulation of Bohr*s Correspondence Principle, Heisenberg (June 1925) discovered the rules governing the behaviour of quantum-theoretical magnitudes.In fall 1925 Born, Heisenberg and Jordan and, independently, Dirac, formulated consistent algebraic schemes of quantum mechanics.Early in 1926 Schrodinger developed wave mechanics.In quick succession were discovered : Bora's probability interpretation of the wave function, the transformation theory of Dirac, Jordan and E. London, Heisenberg's uncertainty relations and Bohr's principle of complementarity.By September 1927 the basis of a complete theory of atomic phenomena had been established.Aspects of this development, in which Heisenberg played a central role, will be presented as a tribute to his memory.

•Jan 1, 1976•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
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.
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.
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.
Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.
Our modern understanding of atoms, molecules, solids, atomic nuclei, and elementary particles is largely based on quantum mechanics. Quantum mechanics grew in the mid-1920s out of two independent developments: the matrix mechanics of Werner and the wave mechanics of Erwin Schrödinger. For the most part this chapter follows the path of wave mechanics, which is more convenient for all but the simplest calculations. The general principles of the wave mechanical formulation of quantum mechanics are laid out and provide a basis for the discussion of spin, identical particles. and scattering processes. The general principles are supplemented with the canonical formalism to work out the Schrödinger equation for charged particles in a general electromagnetic field. The chapter ends with the unification of the approaches of wave and matrix mechanics by Paul Dirac, and a modern approach, known as Hilbert space, is briefly described.
In an attempt to give an exact mathematical formulation of Bohr*s Correspondence Principle, Heisenberg (June 1925) discovered the rules governing the behaviour of quantum-theoretical magnitudes.In fall 1925 Born, Heisenberg and Jordan and, independently, Dirac, formulated consistent algebraic schemes of quantum mechanics.Early in 1926 Schrodinger developed wave mechanics.In quick succession were discovered : Bora's probability interpretation of the wave function, the transformation theory of Dirac, Jordan and E. London, Heisenberg's uncertainty relations and Bohr's principle of complementarity.By September 1927 the basis of a complete theory of atomic phenomena had been established.Aspects of this development, in which Heisenberg played a central role, will be presented as a tribute to his memory.
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.