Path Integral Solution of Non-Central Potential

Abstract

In this paper, we calculate the propagator of a system of particle moving in a class of non-central potential. This study is done in the framework of path integrals. It has been possible to treat this potential in spherical coordinates thanks to the introduction of the system energy by means of the Green's function and with the help of an appropriate temporal transformation which ensures the separation of angular and radial parts. The propagator is then expressed as a product of two partial kernels. The angular kernel is related to the triangular Pöschl-Teller potential while the radial one describes the motion with the oscillator plus inverse square potential. The energy spectrum and the normalized wave functions of the bound states can then be obtained. Particular cases of this potential have also been deduced