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.

Introduction to Volume One

2019 ◽  
pp. 1-42
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Theory ◽  
Black Body ◽  
Black Body Radiation ◽  
Quantum Model ◽  
Light Quantum ◽  
Quantum Hypothesis ◽  
Specific Heats ◽  
Adiabatic Principle ◽  
Old Quantum Theory ◽  
Energy And Momentum

We provide an overview, as non‐technical as possible, of the contents of Vol. 1 of the book. Reflecting the structure of the volume, this overview consists of two parts. In the first part, we summarize the most important early contributions to quantum theory (covered in detail in Chs. 2–4). This part starts with Planck’s work on black‐body radiation culminating in the introduction of Planck’s constant in 1900. It then moves on to Einstein’s 1905 light‐quantum hypothesis, his theory of specific heats, and his formulas for energy and momentum fluctuations in black‐body radiation. After summarizing Bohr’s path to his quantum model of the atom, it concludes with Einstein’s 1916–17 radiation theory combining elements of Bohr’s model with his own light‐quantum hypothesis. In the second part we summarize our analysis of the old quantum theory (given in detail in Chs. 5–7). After a brief overview of the career of Sommerfeld, who together with Bohr took the lead in developing the old quantum theory, we review the three principles we have identified as the cornerstones of the theory (the quantization conditions, the adiabatic principle, and the correspondence principle). We then discuss three of the theory’s most notable successes (fine structure, Stark effect, X‐ray spectra) and, finally, three of its most notorious failures (multiplets, Zeeman effect, helium).

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.

Einstein, Equipartition, Fluctuations, and Quanta

2019 ◽  
pp. 84-142
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Theory ◽  
Statistical Mechanics ◽  
Black Body ◽  
Black Body Radiation ◽  
Light Quantum ◽  
Quantum Hypothesis ◽  
Specific Heats ◽  
Light Quanta ◽  
Physics Community ◽  
Equipartition Theorem

After three papers on statistical mechanics, mostly duplicating work by Boltzmann and Gibbs, Einstein relied heavily on arguments from statistical mechanics in the most revolutionary of his famous 1905 papers, the one introducing the light‐quantum hypothesis. He showed that the equipartition theorem inescapably leads to the classical Rayleigh‐Jeans law for black‐body radiation and the ultraviolet catastrophe (as Ehrenfest later called it). Einstein and Ehrenfest were the first to point this out but the physics community only accepted it after the venerable H.A. Lorentz, came to the same conclusion in 1908. The central argument for light quanta in Einstein’s 1905 paper involves a comparison between fluctuations in black‐body radiation in the Wien regime and fluctuations in an ideal gas. From this comparison Einstein inferred that black‐body radiation in the Wien regime behaves as a collection of discrete, independent, and localized particles. We show that the same argument works for non‐localized quantized wave modes. Although nobody noticed this flaw in Einstein’s reasoning at the time, his fluctuation argument, and several others like it, failed to convince anybody of the reality of light quanta. Even Millikan’s verification of Einstein formula for the photoelectric effect only led to the acceptance of the formula, not of the theory behind it. Einstein’s quantization of matter was better received, especially his simple model of a solid consisting of quantized oscillators. This model could explain why the specific heats of solids fall off sharply as the temperature is lowered instead of remaining constant as it should according to the well‐known Dulong‐Petit law, which is a direct consequence of the equipartition theorem. The confirmation of Einstein’s theory of specific heats by Nernst and his associates was an important milestone in the development of quantum theory and a central topic at the first Solvay conference of 1911, which brought the fledgling theory to the attention of a larger segment of the physics community. Returning to the quantum theory after spending a few years on the development of general relativity, Einstein combined his light‐quantum hypothesis with elements of Bohr’s model of the atom in a new quantum radiation theory.

Satyendra Nath Bose, 1 January 1894 - 4 February 1974

1975 ◽  
Vol 21 ◽  
pp. 116-154 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Intellectual Development ◽  
Albert Einstein ◽  
Wave Mechanics ◽  
Ideal Gases ◽  
Old Quantum Theory ◽  
Modern Physics ◽  
Bose Einstein ◽  
Point Of Departure

S. N. Bose was one of India’s most eminent scientists. Bose’s achievements in scientific research were not as sustained or as numerous as those of his contemporaries like C. V. Raman, (1) Meghnad Saha (2) and K. S. Krishnan, (3) together with whom he became a pioneer of education and research in modern physics in India. But the circumstances of Bose’s intellectual development were unusual and he was destined to play an inspiring role in the scientific and cultural life of his country. Bose’s novel derivation of Planck’s radiation formula, the only significant contribution which he made to physics, came at a turning point between the old quantum theory of Planck, Einstein, Bohr and Sommerfeld and the new quantum mechanics of Heisenberg, Dirac and Schrodinger. Bose sent his paper early in June 1924 to Albert Einstein who recognized its merit, translated it into German, and had it published in the Zeitschrift für Physik [6]. During the summer of 1924 Einstein also received, from Paul Langevin in Paris, a copy of the doctoral thesis of Louis de Broglie (4) dealing with the wave aspects of matter. Bose’s work became the point of departure for Einstein’s investigation on the quantum theory of monatomic ideal gases and ‘gas degeneracy’, leading to his prediction of the condensation phenomenon. (5) Einstein recognized the importance of de Broglie’s ideas and also made use of them in his investigation. (5) In turn, these papers of de Broglie and Einstein stimulated Schrodinger (6) to develop his wave mechanics. The ‘Bose-Einstein statistics’ immediately fitted into the framework of quantum mechanics and enshrined Bose’s name in physics for ever. Bose lived the legend of this fateful encounter with Einstein throughout the rest of his life.

The Physical World

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Variational Principles ◽  
Black Body ◽  
Black Body Radiation ◽  
Physical World ◽  
Atomic Scale ◽  
Solid State Physics ◽  
Least Action ◽  
Dimensional Spacetime

The book is an inspirational survey of fundamental physics, emphasizing the use of variational principles. Chapter 1 presents introductory ideas, including the principle of least action, vectors and partial differentiation. Chapter 2 covers Newtonian dynamics and the motion of mutually gravitating bodies. Chapter 3 is about electromagnetic fields as described by Maxwell’s equations. Chapter 4 is about special relativity, which unifies space and time into 4-dimensional spacetime. Chapter 5 introduces the mathematics of curved space, leading to Chapter 6 covering general relativity and its remarkable consequences, such as the existence of black holes. Chapters 7 and 8 present quantum mechanics, essential for understanding atomic-scale phenomena. Chapter 9 uses quantum mechanics to explain the fundamental principles of chemistry and solid state physics. Chapter 10 is about thermodynamics, which is built around the concepts of temperature and entropy. Various applications are discussed, including the analysis of black body radiation that led to the quantum revolution. Chapter 11 surveys the atomic nucleus, its properties and applications. Chapter 12 explores particle physics, the Standard Model and the Higgs mechanism, with a short introduction to quantum field theory. Chapter 13 is about the structure and evolution of stars and brings together material from many of the earlier chapters. Chapter 14 on cosmology describes the structure and evolution of the universe as a whole. Finally, Chapter 15 discusses remaining problems at the frontiers of physics, such as the interpretation of quantum mechanics, and the ultimate nature of particles. Some speculative ideas are explored, such as supersymmetry, solitons and string theory.

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

1999 ◽  
Vol 13 (02) ◽  
pp. 161-189
Author(s):  
C. SYROS
Keyword(s):  
Quantum Mechanics ◽  
Radiation Spectrum ◽  
Black Body ◽  
Boltzmann Distribution ◽  
Black Body Radiation ◽  
Planck Constant ◽  
Klein Gordon ◽  
Energy Variable ◽  
Liouville’S Theorem ◽  
Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

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.

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