Integrale de chemin et probleme dependant du temps.

Abstract

We know that the path integral formulation is currently a modern way of comprehension and analysis of the physical phenomena since the only tools necessary to this formalism are the usual rudiments of the classical mechanics such as the action and trajectory, we want to test the simplicity of this formulation, on two problems: The first concerns quantum systems with variable mass and potential (depending solely on the position), and the second one with the quantum systems with variable mass and variable potential both dependent on time in addition to position. For the first problem a hermetic form is chosen for the Hamiltonian operator, and after construction of the propagator and application of a space-time transformation, the Green function is obtained. Particular masses were also considered, which made it possible to make comparison with other results obtained differently. For the second problem depends on time, the Green function is also obtained, first by construction and then by a combination of canonical transformation and point transformation and finally for a choice of particular (nonquadratic) forms for the potential V and for the mass m, the dissipative system is then reduced to the conservative one. Note that this problem has been considered in two different ways by the Hamiltonian formulation (canonical transformation) and Lagrange formulation. The results obtained differ in both cases. Further clarification on the procedure will be needed.