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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2007 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2007
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147218 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem / M. Moshinsky, E. Sadurní, Adolfo del Campo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147218 |
|---|---|
| record_format |
dspace |
| spelling |
Moshinsky, M. Sadurní, E. del Campo, A. 2019-02-13T19:15:47Z 2019-02-13T19:15:47Z 2007 Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem / M. Moshinsky, E. Sadurní, Adolfo del Campo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81V35; 81Q05 https://nasplib.isofts.kiev.ua/handle/123456789/147218 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. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). One of the authors (A. del Campo) would like to express his thanks for the hospitality of the Instituto de F´ısica and the support both from the Instituto de F´ısica and of CONACYT (Project No. 40527F) for the time he spent in Mexico. This author would also like to thank the Basque Government (BFI04.479) for financial support. E. Sadurn´ı is grateful to CONACYT and its support through Beca-Cr´edito 171839. M. Moshinsky is grateful to his secretary Fanny Arenas for the capture of this manuscript and the 300 she has done previously. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem |
| spellingShingle |
Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem Moshinsky, M. Sadurní, E. del Campo, A. |
| title_short |
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_sort |
alternative method for determining the feynman propagator of a non-relativistic quantum mechanical problem |
| author |
Moshinsky, M. Sadurní, E. del Campo, A. |
| author_facet |
Moshinsky, M. Sadurní, E. del Campo, A. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147218 |
| citation_txt |
Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem / M. Moshinsky, E. Sadurní, Adolfo del Campo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. |
| work_keys_str_mv |
AT moshinskym alternativemethodfordeterminingthefeynmanpropagatorofanonrelativisticquantummechanicalproblem AT sadurnie alternativemethodfordeterminingthefeynmanpropagatorofanonrelativisticquantummechanicalproblem AT delcampoa alternativemethodfordeterminingthefeynmanpropagatorofanonrelativisticquantummechanicalproblem |
| first_indexed |
2025-12-07T13:29:39Z |
| last_indexed |
2025-12-07T13:29:39Z |
| _version_ |
1850856365869760512 |