Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/110/ |
| _version_ | 1818040934840926208 |
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| author | Marcos Moshinsky Emerson Sadurní Adolfo del Campo |
| author_facet | Marcos Moshinsky Emerson Sadurní Adolfo del Campo |
| author_sort | Marcos Moshinsky |
| collection | DOAJ |
| description | A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators. |
| first_indexed | 2024-12-10T08:22:25Z |
| format | Article |
| id | doaj.art-8069593e738c48f6b47703af7d04d509 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-10T08:22:25Z |
| publishDate | 2007-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-8069593e738c48f6b47703af7d04d5092022-12-22T01:56:18ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-11-013110Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical ProblemMarcos MoshinskyEmerson SadurníAdolfo del CampoA direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators.http://www.emis.de/journals/SIGMA/2007/110/propagatorGreen functionsharmonic oscillator |
| spellingShingle | Marcos Moshinsky Emerson Sadurní Adolfo del Campo Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem Symmetry, Integrability and Geometry: Methods and Applications propagator Green functions harmonic oscillator |
| title | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| title_full | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| title_fullStr | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| title_full_unstemmed | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| title_short | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| title_sort | alternative method for determining the feynman propagator of a non relativistic quantum mechanical problem |
| topic | propagator Green functions harmonic oscillator |
| url | http://www.emis.de/journals/SIGMA/2007/110/ |
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