The Jacobi principal function in quantum mechanics

The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points - qk and pk+1 or pk and qk+1 - through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes....

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Autor principal: Ferraro, Rafael
Publicado: 1999
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03054470_v32_n13_p2589_Ferraro
http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_03054470_v32_n13_p2589_Ferraro2023-06-08T15:30:44Z The Jacobi principal function in quantum mechanics Ferraro, Rafael The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points - qk and pk+1 or pk and qk+1 - through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes. When the measure is chosen to reflect the geometrical character of the propagator (it must behave as a density of weight 1/2 in both of its arguments), the resulting infinitesimal propagator is cast in the form of an expansion in a basis of short-time solutions of the wave equation, associated with the eigenfunctions of the initial momenta canonically conjugated to a set of normal coordinates. The operator ordering induced by this prescription is a combination of a symmetrization rule coming from the phase, and a derivative term coming from the measure. Fil:Ferraro, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1999 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03054470_v32_n13_p2589_Ferraro http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points - qk and pk+1 or pk and qk+1 - through the invariant complete solution of the Hamilton-Jacobi equation associated with the classical path defined by these extremes. When the measure is chosen to reflect the geometrical character of the propagator (it must behave as a density of weight 1/2 in both of its arguments), the resulting infinitesimal propagator is cast in the form of an expansion in a basis of short-time solutions of the wave equation, associated with the eigenfunctions of the initial momenta canonically conjugated to a set of normal coordinates. The operator ordering induced by this prescription is a combination of a symmetrization rule coming from the phase, and a derivative term coming from the measure.
author Ferraro, Rafael
spellingShingle Ferraro, Rafael
The Jacobi principal function in quantum mechanics
author_facet Ferraro, Rafael
author_sort Ferraro, Rafael
title The Jacobi principal function in quantum mechanics
title_short The Jacobi principal function in quantum mechanics
title_full The Jacobi principal function in quantum mechanics
title_fullStr The Jacobi principal function in quantum mechanics
title_full_unstemmed The Jacobi principal function in quantum mechanics
title_sort jacobi principal function in quantum mechanics
publishDate 1999
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03054470_v32_n13_p2589_Ferraro
http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro
work_keys_str_mv AT ferrarorafael thejacobiprincipalfunctioninquantummechanics
AT ferrarorafael jacobiprincipalfunctioninquantummechanics
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