The Principles of Quantum Mechanics

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The Principles of Quantum Mechanics is an influential monograph on quantum mechanics by Paul Dirac , first published in 1930 by Oxford University Press . At the same time, the book was one of the first textbooks on quantum mechanics.

Dirac in Chicago in 1929

background

Dirac was one of the founders of the then new quantum mechanics in Cambridge between 1925 and 1927. His book was based on a series of lectures on quantum mechanics given by Dirac at Cambridge. His lecture from the summer semester (Easter Term) in Cambridge in 1926, which he gave as a doctoral student under Ralph Fowler , was the first lecture on quantum mechanics at a British university and, like the following regular lectures, formed the basis for the book. The first lecture was attended by the later famous physicists Robert Oppenheimer , Douglas Hartree and Nevill Mott , and William McCrea, who attended the lecture, confirmed that the content essentially corresponded to that of the later book, as far as the theory was already developed . The first edition is also very similar to Dirac's lecture notes 1927/28. The description in his book was generally regarded as a masterpiece as soon as it was published, for example in the statements of Wolfgang Pauli and Albert Einstein , who later preferred to consult on questions of quantum mechanics, even if he fundamentally rejected quantum mechanics. Einstein described Dirac's presentation in 1931 as the most logically perfect presentation of quantum theory and for Dirac, too, it was primarily about the presentation of the abstract, logically coherent formalism and how one could predict experimental quantities from it, not about philosophical questions of interpretation or the motivation of the theory from the experiment or via historical embedding. In the foreword of the first edition he wrote that the new theories would be built on the basis of physical concepts that can not be explained by things that the student already knows and that cannot even be adequately described by words . Dirac followed his book closely in his lectures on quantum mechanics. In Cambridge, in addition to Dirac's regular course, which usually fell in the spring trimester, in the 1930s there was a more practical course (based on the use of the Schrödinger equation) by Alan Herries Wilson in the fall trimester.

The idea for publication as a book came from James Gerald Crowther of Oxford University Press , who wanted the book to be the first volume in a new series International Series of Monographs on Physics (edited by Ralph Fowler, Pjotr ​​Kapitza). Dirac began writing the book in 1928, but publication was delayed as Dirac was busy elsewhere. The foreword is dated May 29, 1930. The book was a great success and 2000 copies of the first edition were sold. The later editions also sold well and it was read not only by students but also by experienced physicists. A German translation by Werner Bloch was published by Hirzel-Verlag in 1930. In a meeting, Walter Heitler praised the original approach, but the abstract representation based on the q-number method developed by Dirac is not very suitable as a first introduction, but only for those who are already familiar with matrix or wave mechanics. The German translation sold well, as did the Russian translation (1932). The Russian translation was edited by Dmitri Dmitrijewitsch Iwanenko , with whom Dirac was in contact, and was by Matwei Bronstein . At the request of the Russian editors, it contained additions to applications (Hartree-Fock method) and appendices by Iwanenko as well as additional footnotes by Bronstein. In a few months 3,000 copies were sold and in 1937 a translation of the second edition, edited by Bronstein, appeared. A French translation appeared in 1931 and a Japanese translation of the second edition in 1936.

The first edition received generally positive reviews. Robert Oppenheimer praised the uniform, coherent and astonishingly complete presentation, Wolfgang Pauli saw it in 1931 as an indispensable standard work in the natural sciences , in which he liked the abstract, generally applicable and elegant presentation, but which he also saw the danger of being too far from the experiment remove. In addition, Pauli missed a presentation of the interpretation of quantum mechanics, especially the need for classical measuring instruments. Werner Heisenberg said in a review in the metal industry that Dirac would present quantum mechanics with his symbolic method in a more abstract way than necessary and go into too little detail on applications that are only presented to illustrate the general principles. In the Bulletin of the American Mathematical Society, Bernard Koopman criticized the educational quality, but also the mathematical clarity (compared to the book by John von Neumann ) and also criticized the establishment of the mathematical terms Eigenvalue and Eigenfunction , which then prevailed in English and after the German Concepts eigenvalue and eigenfunction were formed. In the foreword of his book Mathematical Foundations of Quantum Mechanics from 1932, John von Neumann wrote that Dirac had given a representation that could hardly be surpassed in brevity and elegance, which, like the representation using operators in the Hilbert space, was invariant , but this would not meet the requirements of mathematical rigor in any way Wise justice, even if these are naturally and cheaply reduced to the usual level in theoretical physics .

Dirac looked after a total of four (or five) editions, the 2nd edition in 1935, then in 1947 (3rd edition), 1958 (4th edition) and 1967 (revised 4th edition).

content

Quantum mechanics is developed by Dirac in his book from basic principles. Separate chapters are devoted to perturbation theory (Chapter 7), scattering theory (Chapter 8), systems with several particles of the same type (Chapter 9), radiation theory (Chapter 10), relativistic electron theory (Chapter 11, with Dirac equation ) and quantum electrodynamics (Chapter 12).

The second edition - completed in a sabbatical year at Princeton - was less mathematical and easier to read than the first, while maintaining the basic structure, but still had a reputation for being heavy-duty for most students but the most gifted and as a textbook for the practical instruction in quantum mechanics not very suitable. Theoretical physicist Freeman Dyson recalled that Dirac stuck closely (almost verbatim) to his book in lectures and referred to questions about the book. In an interview, Dyson said that at that time he neither learned quantum mechanics from the book, which he had read in the first edition as a student in Winchester without understanding it, nor from the lectures in Cambridge. Dyson thought it was unsuitable for beginners because it gave him no idea of ​​the physical content of quantum mechanics.

From the third edition he uses his formalism of Bra-Ket vectors, which he first introduced in 1939, but which only became generally known with the third edition of Dirac's book. The delta function (Section 15 is dedicated to it) also played a special role in Dirac's mathematical formalism, and this too became particularly well-known through his quantum mechanics textbook (it is an example of generalized functions later called distributions by mathematicians ).

In the 4th edition in 1958 (on which he had worked for a large part of 1956) the chapter on quantum electrodynamics (Chapter 12) was completely revised (in particular the possibility of generating pairs of electron and positron was taken into account), and in the revised 4th edition 1967 added again.

He did not take into account more recent developments, for example in quantum electrodynamics from the 1940s (for which Julian Schwinger , Richard Feynman and Tomonaga received the Nobel Prize) - he basically thought little of these developments ( renormalization ), since, in his opinion, they were those in theory occurring infinities would sweep under the carpet.

In paragraph 32 ( The action principle ) he also deals with path integrals and in the following paragraph ( The Gibbs Ensemble ) the density matrix , referring to John von Neumann .

He deals with the harmonic oscillator with creation and annihilation operators and similarly with ladder operators he also deals with the quantum mechanics of angular momentum. Fermi's golden rule can be found in the chapter on perturbation theory (p. 180). Many of the concepts in the book were created by Dirac himself a few years earlier, such as the so-called second quantization and the Fermi-Dirac statistics , but also his transformation theory (with which he showed the equivalence of Heisenberg's and Schrödinger's formulation of quantum mechanics) and the correspondence of quantum mechanical commutation relations and Poisson brackets .

The book does not contain a single diagram or drawing on its 314 pages (4th edition 1967). It also doesn't include any practice exercises. There are also no historical discussions or explanatory calculations or motivations through experiments. In Chapter 6 (Elementary Applications, from p. 136 in the 4th edition), the first chapter after the chapters with the presentation of the fundamentals of the theory, only the harmonic oscillator, angular momentum and electron spin as well as the hydrogen atom (and selection rules) are dealt with. There are hardly any references to literature - in the final chapter (p. 311) he refers to Walter Heitler 's Quantum theory of radiation (Clarendon Press 1954) and his own Lectures on Quantum Field Theory (Academic Press 1966) for the presentation of applications .

literature

  • Paul Dirac The Principles of Quantum Mechanics , 4th Edition, The International Series of Monographs on Physics 27, Oxford Science Publications, Oxford University Press 1988, ISBN 0198520115
  • Graham Farmelo: The strangest man: The Hidden Life of Paul Dirac, Mystic of the Atom , Faber & Faber, London 2009
  • Helge Kragh Dirac, a scientific biography , Cambridge University Press 1990
  • Laurie Brown , Helmut Rechenberg P. AM Dirac (1930) and J. von Neumann (1932), Books on Quantum Mechanics , in Ivor Grattan-Guinness Landmark Writings in Western Mathematics , Elsevier 2005, chapter 69
  • Laurie Brown: Paul AM Dirac's The Principles of Quantum Mechanics , Physics in Perspective, Volume 8, 2006, pp. 381-407

Web links

Individual evidence

  1. ↑ The elementary quantum mechanics by Max Born and Pascual Jordan appeared in 1930, Werner Heisenberg 's Physical Principles of Quantum Theory in 1930, from the mathematical side Hermann Weyl Group Theory and Quantum Mechanics in 1928, the book Mathematical Foundations of Quantum Mechanics by John von Neumann appeared in 1932, and Wolfgang Pauli ´s article wave mechanics in the manual of physics 1933
  2. ^ Helge Kragh , Paul Dirac and The Principles of Quantum Mechanics , in: Massimiliano Baudino, Research and Pedagogy. A History of Quantum Physics through Its Textbooks , 2013, Edition Open Access
  3. ↑ Graham Farmelo The Strangest Man , Chapter 14.
  4. ↑ Farmelo, Strangest Man. The original citation is in Einstein: Maxwell's Influence on the Development of the Conception of Physical Reality, in: JJ Thompson (Ed.), James Clerk Maxwell. A Commemoration Volume , Cambridge University Press, p. 71
  5. ↑ Dirac was fundamentally averse to such considerations, but was, as he let shine through at various points in his book, a supporter of the Copenhagen interpretation in the sense of Niels Bohr.
  6. ↑ For example, in the Dirac obituary in the Times Online
  7. ↑ W. Heitler: The principles of quantum mechanics. From Dr. P. Dirac. Translated by W. Bloch, Berlin. Verlag S. Hirzel, Leipzig 1930. Price RM. 18, -, RM. 20, -. In: Journal for Applied Chemistry. 44, 1931, p. 209, doi : 10.1002 / ange.19310441114 .
  8. ^ Oppenheimer, Review in Physical Review, Volume 37, 1931, p. 97
  9. ↑ Wolfgang Pauli, Review in Die Naturwissenschaften, Volume 19, 1931, p. 188
  10. ↑ Werner Heisenberg, Review in Metallwirtschaft, Volume 9, 1930, p. 988
  11. ^ Bernard Koopman, Review in Bulletin of the American Mathematical Society, Volume 37, 1931, pp. 495-496, and for the second edition, Bulletin AMS, Volume 42, 1936, pp. 472-474
  12. ↑ John von Neumann, Mathematical Foundations of Quantum Mechanics, Springer 1932, p. 2
  13. ↑ Chapter and page numbers refer to the 4th edition 1967 and its reprints
  14. ↑ Farmelo The Strangest Man , Chapter 19
  15. ↑ Crowther, Great Physicists, Oxford University Press 2004, p. 389
  16. ↑ Dirac A New Notation for Quantum Mechanics , Proceedings of the Cambridge Philosophical Society, Volume 35, 1939, pp. 416-418
  17. ↑ Farmelo Strangest Man . The foreword is dated May 1957
  18. ↑ 357 pages in the first edition
  19. ↑ Otherwise only the following references can be found: Earle Hesse Kennard and Charles Galton Darwin regarding the dissolution of the wave function p. 125, an essay by Van Vleck p. 128 and by Schrödinger p. 261 as well as the classical works by Schrödinger p. 157 (Annalen der Physics 1926, hydrogen atom), Einstein's Stimulated Emission p. 177, the Born-Heisenberg-Jordan essay from 1925 p. 172 and the Lorenz calibration according to Enrico Fermi from his essay in the Reviews of Modern Physics 1932 on p. 287