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Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem
Інший ID:
2000 Mathematics Subject Classification: 81V35; 81Q05
Посилання:
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.
Підтримка:
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.
Дата:
2007
Переглядів:
642
Завантажень:
259
Анотація:
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.
