Failures

2019 ◽  
pp. 300-382
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Ground State Energy ◽  
Ground State ◽  
Equations Of Motion ◽  
Zeeman Effect ◽  
Stationary States ◽  
Old Quantum Theory ◽  
History Of ◽  
Anomalous Zeeman Effect

We consider three topics which proved frustratingly resistant to the methods of the old quantum theory up to the point of emergence of the quantum mechanics of Heisenberg and collaborators in late 1925. First, the old theory could not account convincingly for the superfluity of stationary states implied by the existence of the complex multiplets seen in most atomic spectra. Second, the progressively more complicated theories proposed for explaining the splittings of lines in the anomalous Zeeman effect were found to lead inevitably to glaring inconsistencies with the assumed mechanical equations of motion. Finally, there was the problem of the dual spectrum of helium, and even more basically, of the ground state energy of helium, all calculations of which in terms of specified electron orbits gave incorrect results. We relate the tangled history of the efforts to provide a theoretical resolution of these problems within the old quantum theory.

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.

Transmitting Knowledge across Divides

2016 ◽  
Vol 46 (3) ◽  
pp. 313-359 ◽  
Author(s):  
Marta Jordi Taltavull
Keyword(s):  
Experimental Data ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Scientific Understanding ◽  
Resonance Model ◽  
Optical Dispersion ◽  
History Of

One model, the resonance model, shaped scientific understanding of optical dispersion from the early 1870s to the 1920s, persisting across dramatic changes in physical conceptions of light and matter. I explore the ways in which the model was transmitted across these conceptual divides by analyzing the use of the model both in the development of theories of optical dispersion and in the interpretation of experimental data. Crucial to this analysis is the integration of the model into quantum theory because of the conceptual incompatibility between the model and quantum theory. What is more, a quantum understanding of optical dispersion set the grounds for the emergence of the first theories of quantum mechanics in 1925. A long-term history of the model’s transmission from the 1870s to the 1920s illuminates the ways in which the continuity of knowledge is possible across these discontinuities.

Subsequent and Subsidiary? Rethinking the Role of Applications in Establishing Quantum Mechanics

2015 ◽  
Vol 45 (5) ◽  
pp. 641-702 ◽  
Author(s):  
Jeremiah James ◽  
Christian Joas
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Mechanics ◽  
Theory Construction ◽  
Science Pedagogy ◽  
Old Quantum Theory ◽  
The Common ◽  
Complete Quantum

As part of an attempt to establish a new understanding of the earliest applications of quantum mechanics and their importance to the overall development of quantum theory, this paper reexamines the role of research on molecular structure in the transition from the so-called old quantum theory to quantum mechanics and in the two years immediately following this shift (1926–1928). We argue on two bases against the common tendency to marginalize the contribution of these researches. First, because these applications addressed issues of longstanding interest to physicists, which they hoped, if not expected, a complete quantum theory to address, and for which they had already developed methods under the old quantum theory that would remain valid under the new mechanics. Second, because generating these applications was one of, if not the, principal means by which physicists clarified the unity, generality, and physical meaning of quantum mechanics, thereby reworking the theory into its now commonly recognized form, as well as developing an understanding of the kinds of predictions it generated and the ways in which these differed from those of the earlier classical mechanics. More broadly, we hope with this article to provide a new viewpoint on the importance of problem solving to scientific research and theory construction, one that might complement recent work on its role in science pedagogy.

Quantum Mechanics and the Periodic Table

2019 ◽  
Author(s):  
Eric Scerri
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Periodic Table ◽  
Chemical Properties ◽  
Pauli Exclusion Principle ◽  
Niels Bohr ◽  
Exclusion Principle ◽  
Old Quantum Theory ◽  
Set Up ◽  
Three Body

In chapter 7, the influence of the old quantum theory on the periodic system was considered. Although the development of this theory provided a way of reexpressing the periodic table in terms of the number of outer-shell electrons, it did not yield anything essentially new to the understanding of chemistry. Indeed, in several cases, chemists such as Irving Langmuir, J.D. Main Smith, and Charles Bury were able to go further than physicists in assigning electronic configurations, as described in chapter 8, because they were more familiar with the chemical properties of individual elements. Moreover, despite the rhetoric in favor of quantum mechanics that was propagated by Niels Bohr and others, the discovery that hafnium was a transition metal and not a rare earth was not made deductively from the quantum theory. It was essentially a chemical fact that was accommodated in terms of the quantum mechanical understanding of the periodic table. The old quantum theory was quantitatively impotent in the context of the periodic table since it was not possible to even set up the necessary equations to begin to obtain solutions for the atoms with more than one electron. An explanation could be given for the periodic table in terms of numbers of electrons in the outer shells of atoms, but generally only after the fact. But when it came to trying to predict quantitative aspects of atoms, such as the ground-state energy of the helium atom, the old quantum theory was quite hopeless. As one physicist stated, “We should not be surprised . . . even the astronomers have not yet satisfactorily solved the three-body problem in spite of efforts over the centuries.” A succession of the best minds in physics, including Hendrik Kramers, Werner Heisenberg, and Arnold Sommerfeld, made strenuous attempts to calculate the spectrum of helium but to no avail. It was only following the introduction of the Pauli exclusion principle and the development of the new quantum mechanics that Heisenberg succeeded where everyone else had failed.

scholarly journals The theoretical prediction of the physical properties of many electron atoms and ions. Mole refraction, diamagnetic susceptibility, and extension in space

1927 ◽  
Vol 114 (767) ◽  
pp. 181-211 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Nuclear Charge ◽  
Electron Shell ◽  
Small Error ◽  
Screening Constant ◽  
X Ray ◽  
Average Value ◽  
Old Quantum Theory ◽  
Azimuthal Quantum Number

It is customary to express the empirical data concerning term values in the X-ray region by introducing an effective nuclear charge Z eff . e in the place of the true nuclear charge Z e in an equation theoretically applicable only to a hydrogen-like atom. Often a screening constant S is used, defined by the equation Z eff . = Z — S ; and this screening constant is qualitatively explained as due to the action of electrons which are nearer the nucleus than the electron under consideration, and which in effect partially neutralise the nuclear field. Thus the relativistic or magnetic doublet separation may be represented by the equation Δ v = R α 2 / n 3 k ( k — 1) (Z — s 0 ) 4 + ... This equation, including succeeding terms, was obtained originally by Sommer­feld from relativistic considerations with the old quantum theory; the first term, except for the screening constant s0, has now been derived by Heisenberg and Jordanf with the use of the quantum mechanics and the idea of the spinning electron. The value of the screening constant is known for a number of doublets, and it is found empirically not to vary with Z. It has been found possible to evaluate s 0 theoretically by means of the follow­ing treatment: (1) Each electron shell within the atom is idealised as a uniform surface charge of electricity of amount — z i e on a sphere whose radius is equal to the average value of the electron-nucleus distance of the electrons in the shell. (2) The motion of the electron under consideration is then deter­mined by the use of the old quantum theory, the azimuthal quantum number being chosen so as to produce the closest approximation to the quantum mechanics. (3) Since s 0 does not depend on Z, it is evaluated for large values of Z, by expanding in powers of z i /Z and neglecting powers higher than the first, and then comparing the expansion with that of the expression containing Z — s 0 in powers of s 0 /Z. The values of s 0 obtained in this way* are in satis­factory agreement with the empirical ones, the agreement being excellent in the case of orbits of large excentricity, for which the idealisation of the electron shells would be expected to introduce only a small error.

scholarly journals THE PROBLEM OF REALITY IN THE TEXTS OF NIELS BOHR

2019 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Point Of View ◽  
Niels Bohr ◽  
Stationary States ◽  
Physical Processes ◽  
Specific Behavior ◽  
Physical Experiments ◽  
Interpretation Of Quantum Theory ◽  
Philosophical Questions

The article discusses a new understanding of the reality in the 20th century. Since the key figure in these changes was the Danish physicist Niels Bohr, we refer to his early and later articles to analyze the use of the term “reality”. Through an analysis of the terms, it is shown that Bohr describes discoveries in earlier articles that are inconsistent with old concepts in physics, and it is these questions that will further lead him to a new understanding of reality. In the article we also indicate how many times and in what contexts the term “reality” is used. Further, we find that the term “reality” is more common in later articles than in his earlier works (Copenhagen’s interpretation of quantum theory had not yet been formulated at the time of writing the early works). Through the analyzing of usage of certain terms, we show how the emphasis in the early and late Bohr’s articles shifts. For many years, the Danish physicist has sought to clarify quantum theory. In some later articles, we note that the problems affect not only physical, but also other areas of knowledge. We also analyze the use of the term in later articles. This analysis shows how Niels Bohr’s discoveries in the nature of the objects of the micro-world lead him to questions about the nature of reality. How discoveries in the microcosm affect the new conception of reality is best traced in controversy with other physicists. As the most striking example, we took the article “Discussion with Einstein on epistemological problems in atomic physics”. In this article, Bohr describes the specific behavior of micro-objects, features of physical experiments and proves the idea that a fundamentally new (including ontological plan) understanding of physical processes is needed. An analysis of the terms shows that, from Bohr’s point of view, reality itself is as described by its quantum mechanics. We strive to show the evolution of Bohr’s views in the context of how they influenced the revision of all physics. We conclude that the discovery of stationary states in an atom is the first step to rethinking philosophical questions of a nature of reality.

GENERALIZED VARIATIONAL PRINCIPLE IN QUANTUM MECHANICS

1995 ◽  
Vol 09 (22) ◽  
pp. 2899-2936 ◽  
Author(s):  
A.V. SOLDATOV
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Quantum System ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Convergent Sequence ◽  
Upper Bounds ◽  
Generalized Variational Principle ◽  
Quantitative Characteristics

An algorithm is proposed that allows us to derive the convergent sequence of upper bounds for the ground state energy of a quantum system. The algorithm generalizes the well-known variational principle of quantum mechanics and moreover provides qualitative, and under some additional conditions even quantitative, characteristics of the spectrum of a quantum system as a whole.

scholarly journals 1/ε problem in resurgence

2020 ◽  
Author(s):  
Naohisa Sueishi
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Saddle Points ◽  
Integral Formalism ◽  
Resolvent Method ◽  
Divergent Behavior ◽  
The Relationship

Abstract This paper considers the 1/ε problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using resolvent method, It is shown that including not only one complex bion but multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle points contribution and also the relationship between exact WKB and path integral formalism.

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