Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• Main Authors: Moshinsky, M., Sadurní, E., del Campo, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147218
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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.