Introductory Considerations

2018 ◽  
Author(s):  
John von Neumann
Keyword(s):  
Quantum Theory ◽  
Theoretical Description ◽  
Statistical Interpretation ◽  
Wave Mechanics ◽  
Transformation Theory ◽  
Max Born ◽  
Erwin Schrödinger ◽  
Physical Problems ◽  
Starting Point ◽  
New System

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.

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.

scholarly journals Bands in the secondary spectrum of hydrogen

1927 ◽  
Vol 114 (767) ◽  
pp. 293-313 ◽  
Keyword(s):  
Quantum Theory ◽  
Static Model ◽  
Moment Of Inertia ◽  
Initial Moment ◽  
A Value ◽  
Starting Point ◽  
Band Spectra ◽  
The University ◽  
Low Pressures ◽  
Complete Account

Fulcher’s discovery of bands in the secondary spectrum of hydrogen at low pressures proved the starting point of a number of investigations, including those, based on the valuable tables of Merton and Barratt, which have been carried out in the University of St. Andrews. The application of the quantum theory to these bands has been discussed by one of us (H. S. A.), by Curtis, and in particular by Richardson who, partly in association with Tanaka, has added greatly to the number of known regularities and done much to bring them into line with the theory of band spectra. Nevertheless, apart from the Fulcher system, of which Richardson has recently given a very complete account, there remains a very large number of lines which have not yet been classified. One of the present writers (I. S.) has been engaged in a study of the secondary spectrum at higher pressures, and among the regularities which have been selected by this method is a band with head at 4582·58 A. U. and shading towards the violet, which has been described in a recent communication. This band yielded an initial moment of inertia agreeing closely with a value deduced from a static model of triatomic hydrogen, H 3 . This band has since been found to be one of a large number of similar bands which it will be the purpose of this paper to describe. We shall refer to it for convenience as “Band II A , a .”

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