Résumé:
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.
