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( Path integral formulation)
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The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique history for a system with a sum, or functional integral, over an infinity of possible histories to compute a quantum amplitude. The path integral formulation was developed in 1948 by Richard Feynman. Some preliminaries were worked out earlier, in the course of his doctoral thesis work with John Archibald Wheeler. This formulation has proved crucial to the subsequent development of theoretical physics, since it provided the basis for the grand synthesis of the 1970s called the renormalization group which unified quantum field theory with statistical mechanics. If we realize that the Schrödinger equation is essentially a diffusion equation with an imaginary diffusion constant, then the path integral is a method for the enumeration of random walks. For this reason path integrals had also been used in the study of Brownian motion and diffusion before they were introduced in quantum mechanics.
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