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Physica Scripta

Sixty years of quantum wave mechanics

Derrick S. F. Crothers

Published Nov 1, 1989• 5 citations
Publisher

Abstract

We present an inaugural lecture, originally given by the author on 2 June 1987 at the Queen's University of Belfast, but in an edited version, on the topic Sixty years of quantum wave mechanics. A short historical survey is given as an introduction to some of the author's own personal research in the theory of atomic collisions, notably heavy-particle collisions and semiclassical methods.

DOI
10.1088/0031-8949/40/5/009

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Hugh Everett's long thesis was submitted to John Archibald Wheeler, his doctoral thesis advisor, in January 1956 under the title "Quantum Mechanics by the Method of the Universal Wave Function.'' It was retitled "Wave Mechanics Without Probability'' and circulated in April of that year to several prominent physicists, including Niels Bohr. Largely due to the criticism of the long thesis by the Copenhagen colleagues, Everett and his advisor John Wheeler rewrote Everett's thesis in the winter of 1957 to produce a much shorter version, which Everett subsequently defended for his Ph.D. under the title "On the Foundations of Quantum Mechanics.'' While the long thesis was organized around the quantum measurement problem and how it is best solved by pure wave mechanics, the short thesis presented Everett's relative-state formulation of pure wave mechanics more as a suitable theory for the development of quantum gravity, cosmology, and field theory. The short thesis no longer contains Everett's chapter on information theory and correlation, his survey of possible solutions to the measurement problem, or his extended discussion of the nature of physical theories. What remains is a distilled presentation of pure wave mechanics, his principle of the fundamental relativity of states, and his derivation of the standard quantum statistics. The short thesis was retitled for publication in Reviews of Modern Physics in July 1957 as "The 'Relative State' Formulation of Quantum Mechanics.'' The version below closely follows the Reviews of Modern Physics article. The long thesis itself was not published until 1973 in the DeWitt and Graham Princeton University Press anthology. It was published under the title "The Theory of the Universal Wave Function." Although Everett did not publish the long thesis, he nonetheless kept a copy of it, and appears to have returned to it periodically to make changes even after the short thesis appeared in print. This document is a scanned version of Everett's personal copy of his long thesis, with his collected comments and changes.

•May 20, 2011•0 citations
We present an inaugural lecture, originally given by the author on 2 June 1987 at the Queen's University of Belfast, but in an edited version, on the topic Sixty years of quantum wave mechanics. A short historical survey is given as an introduction to some of the author's own personal research in the theory of atomic collisions, notably heavy-particle collisions and semiclassical methods.
This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group representation theory and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate mathematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
This book represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to specific applications. The formulation of quantum theory is explained and supported with illustrations of the general concepts of elementary quantum systems. In addition to traditional topics of nonrelativistic quantum mechanics - including single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, and the theory of angular momentum - the book also covers modern issues, among them quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is also outlined in explanatory notes. Ideal as a supplement to classroom lectures, the book can also serve as a compact and comprehensible refresher of elementary quantum theory for more advanced students.
From January to March 1938 – as we have seen in Chapter 1 – Majorana delivered his only lectures on quantum mechanics at the University of Naples, where he obtained a position as a full professor of theoretical physics. He prepared a set of lecture notes [26] for his students (see Section 13.5), and, among the original manuscripts of these lectures, we find some additional spare papers that cannot be considered as notes for academic lectures, even for an advanced course such as that taught by Majorana. Instead, as suggested in Refs. [328, 329], they probably refer to a seminar or conference held at the University of Naples, whose main topic was likely the theoretical interpretation of the molecular bonding in the framework of quantum mechanics; the notes were prepared by Majorana for his own personal use. Scientific interest in this dissertation, however, focuses not on its main topic, nor on the calculations (which are practically absent from the manuscript), but rather on the interpretation given by Majorana to key concepts of the quantum theory, i.e. the concept of quantum state and the direct application of the quantum theory to the particular case of molecular bonding. The manuscript indeed discloses a peculiar cleverness on the part of Majorana in referring to this pivotal argument of quantum mechanics, and also reveals the concept was at least ten years ahead of its time. This link had been already noted earlier by Nicola Cabibbo [330], who saw in the Majorana manuscript a vague and approximate anticipation of the idea underlying the Feynman interpretation of quantum mechanics in terms of path integrals. A more analytic study has revealed, however, some intriguing surprises, upon which we will focus here. In addition to the historical interest of Majorana's manuscript, we stress also the particularly powerful didactic method used by him on the given subject: his original presentation of the quantum-mechanical problems is exceedingly useful in teaching now those or related topics. For this reason, in the Appendix we will report the entire text (translated from the Italian) as prepared by Majorana.
Hugh Everett's long thesis was submitted to John Archibald Wheeler, his doctoral thesis advisor, in January 1956 under the title "Quantum Mechanics by the Method of the Universal Wave Function.'' It was retitled "Wave Mechanics Without Probability'' and circulated in April of that year to several prominent physicists, including Niels Bohr. Largely due to the criticism of the long thesis by the Copenhagen colleagues, Everett and his advisor John Wheeler rewrote Everett's thesis in the winter of 1957 to produce a much shorter version, which Everett subsequently defended for his Ph.D. under the title "On the Foundations of Quantum Mechanics.'' While the long thesis was organized around the quantum measurement problem and how it is best solved by pure wave mechanics, the short thesis presented Everett's relative-state formulation of pure wave mechanics more as a suitable theory for the development of quantum gravity, cosmology, and field theory. The short thesis no longer contains Everett's chapter on information theory and correlation, his survey of possible solutions to the measurement problem, or his extended discussion of the nature of physical theories. What remains is a distilled presentation of pure wave mechanics, his principle of the fundamental relativity of states, and his derivation of the standard quantum statistics. The short thesis was retitled for publication in Reviews of Modern Physics in July 1957 as "The 'Relative State' Formulation of Quantum Mechanics.'' The version below closely follows the Reviews of Modern Physics article. The long thesis itself was not published until 1973 in the DeWitt and Graham Princeton University Press anthology. It was published under the title "The Theory of the Universal Wave Function." Although Everett did not publish the long thesis, he nonetheless kept a copy of it, and appears to have returned to it periodically to make changes even after the short thesis appeared in print. This document is a scanned version of Everett's personal copy of his long thesis, with his collected comments and changes.