"Application de l’intégrale de chemin à certains systèmes quantiques déformés"

Abstract

"This work concerns the application of the Feynman path integrals method to two dynamical systems interesting theoretical physics and quantum chemistry. In the context of non-relativistic quantum mechanics, we have undertaken a detailed study of the problem of a particle in a general electric potential with axial symmetry. This potential generalizes the ring-shaped oscillator and Hartmann system. The variables are separated completely in polar coordinates. For two specific types of V (r), the energies of the discrete spectrum and the corresponding wave functions are determined.

In the context of relativistic quantum mechanics, we have discussed the problem of a spinless particle of mass M and charge (-e ) in the presence of a vector potential and a scalar potential with spherical symmetry and of general Pöschl -Teller type which depends on a positive deformation parameter q . When q is greater than or equal to unity, the approximate radial Green's function for the l-wave is built in a compact form. For 0 < q < 1, the radial Green's function for the wave s (l = 0), is calculated without approximation by means of the perturbation technique. In both cases, the condition of quantization of energy and the wave functions are obtained. As a special case, when the vector potential and the scalar potential are of Morse type, the energy spectrum and the wave functions are found by passing the limit q →0. "