Etude complète de certains potentiels diatomiques déformés par l'intégrale de chemin de Feynman.

Abstract

This work is concerned with the use of the Feynman path integral formalism for the study of a set of quantum systems subjected to some spherically symmetric deformed diatomic potentials of interest in theoretical physics and in quantum chemistry. In the framework of the nonrelativistic quantum mechanics, we first reviewed the problem of the improved radial Tietz potential that depends on the real parameter q of deformation. Next, we discussed again that of the radial Tietz-Wei potential characterized by the real parameter of deformation - 1< <1. In all cases concerning the deformation parameter, the radial Green’s function in closed form, the energy spectrum and the wave functions of bound states are evaluated. In the context of the relativistic quantum mechanics, the problems of a spinless relativistic particle in the presence of equal vector and scalar potentials, following the exact shape of the q-deformed radial Rosen-Morse potential, the deformed radial Tietz-Wei potential and the deformed improved radial Tietz potential are reexamined. In the different cases, the radial Green function is constructed in closed form. The energy spectra and the wave functions are determined.