From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics

1973 ◽  
pp. 276-293 ◽  
Author(s):  
B. L. van der Waerden
Keyword(s):  
Quantum Mechanics ◽  
Wave Mechanics ◽  
Matrix Mechanics

Oppenheimer's first paper: Molecular band spectra and a professional style

2007 ◽  
Vol 37 (2) ◽  
pp. 247-270 ◽  
Author(s):  
David C. Cassidy
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Spectral Lines ◽  
Molecular Band ◽  
Wave Mechanics ◽  
Infrared Band ◽  
Commutator Algebra ◽  
Matrix Mechanics ◽  
Characteristic Features ◽  
Band Spectra

Beginning early in the 20th century spectroscopists attributed the infrared band spectra emitted by diatomic molecules to quantum vibration and rotation modes of the molecules. Because of these relatively simple motions, band spectra offered a convenient .rst phenomenon to which to apply formulations of the new quan-tum mechanics in 1926. In his .rst paper, completed in Cambridge in May 1926, Oppenheimer presented a derivation of the frequencies and relative intensities of the observed spectral lines on the basis of Paul Dirac's new quantum commutator algebra. At the same time Lucy Mensing published a similar derivation utiliz-ing matrix mechanics, as did Edwin Fues utilizing wave mechanics. Analyses of Oppenheimer's paper and of its historical and scienti.c contexts offer insights into the new quantum mechanics and its utilization and reception during this brief period of competing formalisms, and into the characteristic features of Oppenheimer's later style of research and publication.

scholarly journals Quantum gravity as the unification of general relativity and quantum mechanics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Wave Mechanics ◽  
Matrix Mechanics ◽  
System P

nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the invariance “within – out of” of the same system.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

On the application of quantum mechanics to mortality tables

1942 ◽  
Vol 71 (2) ◽  
pp. 228-258
Author(s):  
R. D Anderson
Keyword(s):  
Quantum Mechanics ◽  
Modern World ◽  
Wave Mechanics ◽  
New Ideas ◽  
The Subject ◽  
Almost All

If you have had your attention directed to the novelties in thought in your own lifetime, you will have observed that almost all really new ideas have a certain aspect of foolishness when they are first produced. Prof. A. N. Whitehead, Science and the Modern World.1. Quantum Mechanics is a portentous name; the alternative—Wave Mechanics—is almost as bad. The mathematics are formidable, the literature large and growing rapidly, and the subjectmatter dealt with is the behaviour of physical things, such as electrons, protons, atoms, and so on. Why, then, should actuaries as such take any interest in the subject?

Quantum Physics

2017 ◽  
Author(s):  
Suman Seth
Keyword(s):  
Quantum Physics ◽  
Subsequent Development ◽  
Atomic Spectroscopy ◽  
Irreversible Processes ◽  
Wave Mechanics ◽  
Matrix Mechanics ◽  
Max Born ◽  
History Of ◽  
Post War ◽  
History Of Quantum Physics

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.

Electron diffraction chez Thomson: early responses to quantum physics in Britain

2010 ◽  
Vol 43 (2) ◽  
pp. 245-275 ◽  
Author(s):  
JAUME NAVARRO
Keyword(s):  
Quantum Mechanics ◽  
Electron Diffraction ◽  
Quantum Physics ◽  
Wave Mechanics ◽  
Basic Tenet ◽  
Wave Particle Duality ◽  
Quantum Wave ◽  
The University ◽  
Total Agreement ◽  
Father And Son

AbstractIn 1927, George Paget Thomson, professor at the University of Aberdeen, obtained photographs that he interpreted as evidence for electron diffraction. These photographs were in total agreement with de Broglie's principle of wave–particle duality, a basic tenet of the new quantum wave mechanics. His experiments were an initially unforeseen spin-off from a project he had started in Cambridge with his father, Joseph John Thomson, on the study of positive rays. This paper addresses the scientific relationship between the Thomsons, father and son, as well as the influence that the institutional milieu of Cambridge had on the early work of the latter. Both Thomsons were trained in the pedagogical tradition of classical physics in the Cambridge Mathematical Tripos, and this certainly influenced their understanding of quantum physics and early quantum mechanics. In this paper, I analyse the responses of both father and son to the photographs of electron diffraction: a confirmation of the existence of the ether in the former, and a partial embrace of some ideas of the new quantum mechanics in the latter.

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