Alguns métodos para o cálculo do propagador de Feynman

Abstract

Here we present a discussion of three methods to calculate the Feynman propagator for some models in non-relativistic quantum mechanics. The formalism of Feynman is just one of several available for addressing problems in quantum mechanics. The first method is a calculation of the integral path, which is based on a recurrence relation for the production of infinitesimal propagators. This recurrence relation has not appeared in previous discussions of the full path of the one-dimensional harmonic oscillator, although inspired by a similar relationship in a three-dimensional system. The second method was developed by Schwinger in 1951 for treating effective action in quantum electrodynamics based on the solution of the equations of motion of the Heisenberg operator. With the proper use of the operator ordained and subordinated the initial conditions produces the propagator. Finally, the third method, which uses the algebraic techniques are based on factorization of the time evolution operator using the formula Baker-Campbell-Hausdorff.