## On the theory of quantum mechanics

FIRST EDITION, SCARCE PRESENTATION OFFPRINT OF ONE OF DIRAC’S MOST IMPORTANT PAPERS: the introduction of what is now known as “Fermi-Dirac statistics”. *On the theory of quantum mechanics* “is justly seen as a major contribution to quantum theory” (Kragh, p. 36). "It introduced [Dirac’s] quantum mechanical derivation of what is now called Fermi-Dirac statistics, which describes a distribution of particles (now known as fermions, a name coined by Dirac in 1945) in certain systems containing many identical particles that obey the Pauli exclusion principle—meaning that no two of the particles can occupy the same quantum state simultaneously. The paper will be remembered as the first in which quantum mechanics is brought to bear on statistical mechanics. Recall that the earliest work on quantum statistics, by Bose and by Einstein, predates quantum mechanics. Also, Fermi’s introduction of the exclusion principle in statistical problems, though published after the arrival of quantum mechanics, is still executed in the context of the ‘old’ quantum theory. All these contributions were given their quantum mechanical underpinnings by Dirac, who was, in fact, the first to give the correct justification of Planck’s law, which started it all” (Pais, p. 6).

Dirac’s paper may also be considered the birth of quantum electrodynamics. He applied Schrödinger’s wave mechanics (his earlier papers had used exclusively Heisenberg’s matrix mechanics) to develop a theory of time-dependent perturbations and applied it to the emission and absorption of radiation. “Radiation theory was the subject of the last section of the important paper ‘On the theory of quantum mechanics.’ There Dirac considered a system of atoms subjected to an external perturbation that could vary arbitrarily with the time. Of course, the particular perturbation he had in mind was an incident electromagnetic field, but, characteristically, he stated the problem in the most general way possible” (Kragh, pp. 120-1).

Dirac and Enrico Fermi discovered Fermi-Dirac statistics independently of one another. Several months before the appearance of Dirac’s paper, Fermi had published his own in which he applied Pauli’s exclusion principle to his theory of an ideal monatomic gas, rather than for general systems of identical fermions, and in the context of the “old” quantum theory, not quantum mechanics. “When he was asked about it several decades later, [Dirac] remarked: ‘I had read Fermi’s paper on Fermi statistics and had forgotten it completely. When I wrote my work on the anti-symmetric wave functions, I did not refer to it at all. Then Fermi wrote and told me and I remembered that I had previously read about it’... Fermi’s letter had the effect that Dirac later on never forgot to mention the priority of his Italian colleague when referring to the statistics obeyed by electrons and the like. In spite of this admitted priority of Fermi it was essentially Dirac’s paper that helped the physicists tremendously in understanding the meaning of the new statistical methods” (Mehra & Rechenberg, p. 767).

“Following the publication of Dirac’s paper, the new statistics was eagerly taken up and applied to a variety of problems. The first application was made by Dirac’s former teacher, Fowler; as an expert in statistical physics, he was greatly interested in the Fermi-Dirac result. Fowler studied a Fermi-Dirac gas under very high pressure, thus beginning a chapter in astrophysics that, a few years later, would be developed into the celebrated theory of white dwarfs by his student Chandrasekhar. In Germany, Pauli and Sommerfeld made other important applications of the new quantum statistics, with which they laid the foundation for the quantum theory of metals in 1927” (Kragh, p. 36).

H. Kragh, *Dirac: A Scientific Biography*; J. Mehra & H. Rechenberg, *The Historical Development of Quantum Theory*, Vol. 5. A. Pais, “Paul Dirac: Aspects of his life and work,” in *Paul Dirac: The Man and his Work*.

PRESENTATION COPY: inscribed “With the author’s compliments” in Dirac’s hand at the top of the front wrapper.

OFFPRINT FROM: Proceedings of the Royal Society A, 112 (1926). London: Harrison & Sons for the Royal Society, 1926. Quarto, original printed wrappers. Light soiling, two small burn-holes in front wrapper (not affecting text); some soiling over inscription. OFFPRINTS OF DIRAC’S MAJOR WORKS ARE EXCEPTIONALLY RARE.

Price: $27,500 .