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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todo:paper_03054470_v32_n13_p2589_Ferraro2023-10-03T15:21:47Z The Jacobi principal function in quantum mechanics Ferraro, R. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Ferraro, R. |
| spellingShingle |
Ferraro, R. The Jacobi principal function in quantum mechanics |
| author_facet |
Ferraro, R. |
| author_sort |
Ferraro, R. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_03054470_v32_n13_p2589_Ferraro |
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AT ferraror thejacobiprincipalfunctioninquantummechanics AT ferraror jacobiprincipalfunctioninquantummechanics |
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1807314479018409984 |