Etude de potentiels polyatomiques par l’intégrale de chemin

Abstract

This work concerns a rigorous treatment by the Feynman path integral of a set containing four spherically symmetric quantum systems studied in the past by means of other ineffective methods. In the framework of nonrelativistic quantum mechanics, the radial RosenMorse potential and the general Schiöberg potential characterized by a real deformation parameter are re-examined by taking into consideration the Dirichlet boundary conditions when formulating the path integral. In each case, the Green’s function is built in closed form. The energy spectrum as well as the wave functions corresponding to the bound states are obtained. In the context of the relativistic quantum mechanics, we first considered the problem of a Dirac particle placed in a vector q-deformed Hulthén potential. For , The Green’s function associated with wave is constructed with the help of a similarity transformation analog with that of Biedenharn and of a space-time transformation, in addition to the choice of an adequate approximation to replace the centrifugal potential term. We then discussed the problems of a Klein-Gordon particle and a Dirac particle subjected in the same time to a vector potential and a scalar potential of the modified Pöschl-Teller-type by considering the Dirichlet boundary conditions. In each case, the Green’s function associated with -waves ( ) is calculated. The energy spectrum and the wave functions are deduced.