الخلاصة:
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.
