
SIGMA 3 (2007), 110, 12 pages arXiv:0711.3544
http://dx.doi.org/10.3842/SIGMA.2007.110
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Alternative Method for Determining the Feynman Propagator of a NonRelativistic 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 20364, 01000 México D.F., México
^{b)} Departamento de QuímicaFísica, 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
Abstract
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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