## Space-Time Approach to Non-Relativistic Quantum Mechanics

"The real foundation of quantum mechanics and thus of physical theory."
– Murray Gell-Mann, 1969 Nobel laureate in Physics

"This is a mathematical formula which I will now show you produces all the results of quantum mechanics."
– Richard Feynman, introducing path integrals at the famous Pocono Conference

First edition, first printing, of Feynman's path integral formalism, his revolutionary approach to solving the fundamental equations of quantum mechanics and the basis for his later famous formulations of "Feynman rules" and "Feynman diagrams"..

"In mid-1947 friends of Feynman persuaded him – threats and cajoling were required – to write for publication the theoretical ideas they kept hearing him explain. When he finally did, he used no diagrams. The result was partly a reworking of his thesis, but it also showed the maturing and broadening of his command of the issues of quantum electrodynamics. He expressed the tenets of his new vision with unabashed plainness. For some physicists this would be the most influential set of ideas Feynman ever published.

"He said he had developed an alternative formulation of quantum mechanics to add to the pair of formulations produced two decades before by Schrodinger and Heisenberg. He defined the notion of probability amplitude for a space-time path. In the classical world one could merely add probabilities... in the quantum world probabilities were expressed as complex numbers, numbers with both a quantity and a phase, and these so-called amplitudes were squared to produce a probability. This was the mathematical procedure necessary to capture the wavelike aspects of particle behavior...

"Probability amplitudes were normally associated with the likelihood of a particle's arriving at a certain place at a certain time. Feynman said he would associate the probability amplitude 'with an entire motion of a particle'- with a path. He stated the central principle of his quantum mechanics: The probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. These complex numbers, these amplitudes, were written in terms of the classical action; he showed how to calculate the action for each path as a certain integral. And he established that this peculiar approach was mathematically equivalent to the standard Schrodinger wave function, so different in spirit.

"The Physical Review had printed nothing by Feynman since his undergraduate thesis almost a decade before. To his dismay, the editors now rejected this paper. Bethe helped him rewrite it, showing him how to spell out for the reader what was old and what was new, and he tried the more retrospective journal Reviews of Modern Physics, where finally it appeared the next spring under the title 'Space-Time Approach to Non-Relativistic Quantum Mechanics'." (Gleick).

FEYNMAN, RICHARD. "Space-Time Approach to Non-Relativistic Quantum Mechanics". In: Reviews of Modern Physics, vol. 20, no. 2 (April 1948): 367–87. Lancaster, PA: American Physical Society, 1948. First edition, first printing. Quarto, original printed wrappers. With neat ownership signature on front wrapper ("H.T. Epstein") of distinguished physicist and biophysicist Herman T. Epstein (1920-2007). Very mild, general wear; a near-fine copy, rare in original wrappers and without any institutional stamps.

Note: A custom cloth box can be made for this item for an additional \$250.

References:

Gleick, James, Genius: The Life and Science of Richard Feynman (New York: Pantheon Books, 1992), p. 247–49).

"Invention of the path integral formalism for quantum mechanics". Ezhela, V.V., Particle Physics: One Hundred Years of Discoveries, An Annotated Chronological Bibliography (Woodbury, NY: American Institute of Physics Press, 1996).

Price: \$7,000 .

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