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- Path_integral_formulation abstract "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 trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude.The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Brownian motion. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac in his 1933 paper. The complete method 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. The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian (rather than a Hamiltonian) as a starting point.This formulation has proven crucial to the subsequent development of theoretical physics, because it is manifestly symmetric between time and space. Unlike previous methods, the path-integral allows a physicist to easily change coordinates between very different canonical descriptions of the same quantum system.The path integral also relates quantum and stochastic processes, and this provided the basis for the grand synthesis of the 1970s which unified quantum field theory with the statistical field theory of a fluctuating field near a second-order phase transition. The Schrödinger equation is a diffusion equation with an imaginary diffusion constant, and the path integral is an analytic continuation of a method for summing up all possible random walks. For this reason path integrals were used in the study of Brownian motion and diffusion a while before they were introduced in quantum mechanics.".
- Path_integral_formulation thumbnail Three_paths_from_A_to_B.png?width=300.
- Path_integral_formulation wikiPageExternalLink index.htm.
- Path_integral_formulation wikiPageExternalLink 63.eprb.ps.
- Path_integral_formulation wikiPageExternalLink b5.
- Path_integral_formulation wikiPageExternalLink pthic10.pdf.
- Path_integral_formulation wikiPageExternalLink website_Chap18.pdf.
- Path_integral_formulation wikiPageExternalLink Path_integral.
- Path_integral_formulation wikiPageID "438476".
- Path_integral_formulation wikiPageRevisionID "606486703".
- Path_integral_formulation align "right".
- Path_integral_formulation hasPhotoCollection Path_integral_formulation.
- Path_integral_formulation quote ""...we see that the integrand in must be of the form where F is a function of , which remains finite as h tends to zero. Let us now picture one of the intermediate qs, say qk, as varying continuously while the other ones are fixed. Owing to the smallness of h, we shall then in general have F/h varying extremely rapidly. This means that will vary periodically with a very high frequency about the value zero, as a result of which its integral will be practically zero. The only important part in the domain of integration of qk is thus that for which a comparatively large variation in qk produces only a very small variation in F. This part is the neighbourhood of a point for which F is stationary with respect to small variations in qk. We can apply this argument to each of the variables of integration ....and obtain the result that the only important part in the domain of integration is that for which F is stationary for small variations in all intermediate qs. ...We see that F has for its classical analogue , which is just the action function which classical mechanics requires to be stationary for small variations in all the intermediate qs. This shows the way in which equation goes over into classical results when h becomes extremely small."".
- Path_integral_formulation source "Dirac op. cit., p. 69".
- Path_integral_formulation width "42".
- Path_integral_formulation subject Category:Concepts_in_physics.
- Path_integral_formulation subject Category:Quantum_field_theory.
- Path_integral_formulation subject Category:Quantum_mechanics.
- Path_integral_formulation subject Category:Statistical_mechanics.
- Path_integral_formulation type Abstraction100002137.
- Path_integral_formulation type Cognition100023271.
- Path_integral_formulation type Concept105835747.
- Path_integral_formulation type Content105809192.
- Path_integral_formulation type FundamentalPhysicsConcepts.
- Path_integral_formulation type Idea105833840.
- Path_integral_formulation type PsychologicalFeature100023100.
- Path_integral_formulation comment "The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics.".
- Path_integral_formulation label "Integral de caminos (mecánica cuántica)".
- Path_integral_formulation label "Integrale sui cammini".
- Path_integral_formulation label "Integração funcional".
- Path_integral_formulation label "Intégrale de chemin".
- Path_integral_formulation label "Padintegraal".
- Path_integral_formulation label "Path integral formulation".
- Path_integral_formulation label "Pfadintegral".
- Path_integral_formulation label "Формулировка квантовой теории через интегралы по траекториям".
- Path_integral_formulation label "経路積分".
- Path_integral_formulation label "路徑積分表述".
- Path_integral_formulation sameAs Pfadintegral.
- Path_integral_formulation sameAs Integral_de_caminos_(mecánica_cuántica).
- Path_integral_formulation sameAs Intégrale_de_chemin.
- Path_integral_formulation sameAs Integrale_sui_cammini.
- Path_integral_formulation sameAs 経路積分.
- Path_integral_formulation sameAs 경로_적분.
- Path_integral_formulation sameAs Padintegraal.
- Path_integral_formulation sameAs Integração_funcional.
- Path_integral_formulation sameAs m.028kt6.
- Path_integral_formulation sameAs Q898323.
- Path_integral_formulation sameAs Q898323.
- Path_integral_formulation sameAs Path_integral_formulation.
- Path_integral_formulation wasDerivedFrom Path_integral_formulation?oldid=606486703.
- Path_integral_formulation depiction Three_paths_from_A_to_B.png.
- Path_integral_formulation isPrimaryTopicOf Path_integral_formulation.
