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

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

2007-11-22

arxiv.org/abs/0711.3544v2

SIGMA 3 (2007), 110, 12 pages

Physics

Quantum Physics

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2007.110

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.

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