The Principles of Quantum Mechanics

This article is about the book by Paul Dirac. For the book by Ramamurti Shankar, see Principles of Quantum Mechanics.

The Principles of Quantum Mechanics

Title page of the first edition
Author	Paul Dirac
Language	English
Subject	Quantum mechanics
Genres	Non-fiction
Publisher	Oxford University Press
Publication date	1930
Publication place	United Kingdom
Media type	Print
Pages	357

The Principles of Quantum Mechanics is an influential monograph written by Paul Dirac and first published by Oxford University Press in 1930. In this book, Dirac presents quantum mechanics in a formal, logically consistent, and axiomatic fashion, making the book the first of its kind. Its 82 sections contain 785 equations with no diagrams. Nor does it have an index, a bibliography, or an list of suggestions for further reading. The first half of the book lays down the foundations of quantum mechanics while the second half focuses on its applications.

History

Paul Dirac played a key role in the development of quantum mechanics at the University of Cambridge and the University of Göttingen during the mid- to late-1920s. The first edition appeared in 1930. Dirac synthesized and improved upon the wave and matrix formulations of quantum mechanics, creating his own version as the theory of linear transformations. He was also inspired by a paper published by Cornelius Lanczos presenting quantum mechanics in terms of the theory of linear integral equations. In the preface, Dirac commented on his work, "A great deal of my work was just playing with equations and see what they give." Dirac also popularized the distribution or generalized function now named after him, the Dirac $\delta$-function, though it had previously been used in the nineteenth century by scholars such as Gustav Kirchhoff in a paper on the Huygens principle in optics and by Oliver Heaviside in his work on electromagnetism.

In the second edition (1935), Dirac aimed to make the book more accessible than the first, and rewrote most of it.He included a new discussion on the action principle, though with a footnote saying that students uninterested in analytical mechanics could skip it, and acknowledged the discovery of the positron, predicted by the negative-energy solution to his relativistic wave equation for the electron.

In 1947 the third edition of the book was published, in which the chapter on quantum electrodynamics was rewritten particularly with the inclusion of electron-positron creation. Beginning with this edition, the mathematical descriptions of quantum states and operators were changed to use the bra–ket notation, introduced in 1939 by Dirac himself.

In the fourth edition, 1958, the same chapter was revised, adding new sections on interpretation and applications. Later a revised fourth edition appeared in 1967. For the last editions, the greatest changes were in the final chapter of the book, a reflection of the rapid pace of development of quantum electrodynamics, both theoretical and experimental.

It has been translated to multiple languages, including Russian, Japanese, German, and French. Dirac supplied an additional preface for the Russian edition, thanks to this good relationship with Russian physicists Igor Tamm and Peter Kapitza. He also supplied a preface to the Japanese edition as requested by the translators, two of whom were Yoshio Nishina and Sin-Itiro Tomonaga.

Contents

• The principle of superposition
• Dynamical variables and observables
• Representations
• The quantum conditions
• The equations of motion
• Elementary applications
• Perturbation theory
• Collision problems
• Systems containing several similar particles
• Theory of radiation
• Relativistic theory of the electron
• Quantum electrodynamics

Reception and legacy

Helge Kragh surveyed reviews by physicists (including Werner Heisenberg, Wolfgang Pauli, and others) from the time of Dirac's book's publication. According to Laurie M. Brown, it "set the stage, the tone, and much of the language of the quantum-mechanical revolution."

The book quickly rose to prominence, surpassing other texts published in the 1930s. Pauli praised it as "an indispensable standard work" but was concerned that it was too distant from experiments. He also had a high opinion of the German translation, describing it and the original book as "highly reliable" and "essential" for physicists studying quantum theory. Paul Epstein and Heisenberg complimented the second edition for being more comprehensible than the first. Albert Einstein admired the book as ­"the most logically perfect presentation" of the subject and made it his companion. Freeman Dyson compared it to a fine work of art. Max Jammer observed that Dirac's primary motivation in writing the book was creating an exposition in physics, treating mathematics as a tool. In this regard, John von Neumann's Mathematical Foundations of Quantum Mechanics (1932), with its uncompromising emphasis on mathematical rigour, was a supplement to Dirac's book. Laurent Schwartz, who put the notion of distributions on a secure mathematical footing in 1945, credited Dirac with thinking of the Dirac delta function as a kernel.

Among students, however, opinions were mixed. Some were displeased that the book was basically a transcript of Dirac's lectures at Cambridge. Most students looked elsewhere because wanted a text that could teach them how to carry out computations. But the most gifted of them viewed the book as a ­"bible" of modern physics. One such student was Subrahmanyan Chandrasekhar, who later became an astrophysicist. Abdus Salam and Eugene Wigner compared Dirac's The Principles of Quantum Mechanics with the Principia, written by Dirac's predecessor as the Lucasian Professor of Mathematics at Cambridge, Isaac Newton. In his doctoral dissertation, Richard Feynman cited Dirac's discussion of the action principle in the second edition. Still in print in the early twenty-first century, it has influenced many generations of young physicists.

See also

• The Evolution of Physics (Einstein and Infeld)
• The Feynman Lectures on Physics Vol. III (Feynman)
• The Physical Principles of the Quantum Theory (Heisenberg)
• Mathematical Foundations of Quantum Mechanics (von Neumann)