Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 110, 12 pages      arXiv:0711.3544
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

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

Marcos Moshinsky a, Emerson Sadurní a and Adolfo del Campo b
a) Instituto de Física Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México D.F., México
b) Departamento de Química-Física, Universidad del País Vasco, Apdo. 644, Bilbao, Spain

Received August 21, 2007, in final form November 13, 2007; Published online November 22, 2007; Misprints are corrected December 06, 2007

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.

Key words: propagator; Green functions; harmonic oscillator.

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