Dynamic study of certain non-relativistic and relativistic problems using the path integral approach

Abstract

In this thesis, it was proved that the formulation of the Feynman path integral plays an important role in solving relativistic and non-relativistic problems in quantum mechanics. To this end, an approximation scheme for the centrifugal term and an appropriate space time of the Duru-Kleinert transformation allow the radial path integral to be converted into a manageable integral. The first part focuses on the prediction of the non-relativistic ro-vibrational energy for the q-deformed modified P?schl-Teller potential, followed by two special cases including the P?schl-Teller type potential and the generalized hyperbolic potential is presented with some diatomic molecules. The predicted values are in better agreement with numerical results and other methods in the literature. The second part deals with the solution of the Klein-Gordon equation under equal scalar and vector modified second type P?schl-Teller potentials. The eigenvalues of the relativistic energy are positive on the basis of a specific condition for the wave functions. In the third part, we solve the Dirac equation for an arbitrary spin-orbit quantum number ? using the q-deformed generalisedP?schl-Teller potential (q-DGPT). The results of the numerical analysis show that there are only bound states with negative energy in the pseudospin symmetry situation with constraint . Moreover, in the non-relativistic limits, the expression for the non-relativistic ro-vibrational energy of the diatomic molecule is derived from the relativistic energy equation in spin symmetry. The results obtained for 39K2 (a3?+u)and CO (X1?+)under Varshni conditions are in good agreement with theoretical and experimental data