Path integral treatment of a Klein Gordon particle with generalized inverse Quadratic Yukawa potential
Salah Eddine Aid, Hocine Boukabcha, Mohamed Hemis
Abstract We solved the Klein–Gordon equation for a generalized inverse quadratic Yukawa (GIQY) potential via path integrals approach. We applied approximations to deal with the terms 1/r 2 and 1/r. A path integral representation of Green’s function relating to a particle moving in a mixture of equal vector and scalar potentials was established. To integrate Green’s function, a space-time transformation was successfully used, and the present problem was reduced to a previously known modified Pöschl-Teller potential problem. The integrated Green’s function contains important information about the considered system, from which we obtained energy eigenvalues and the corresponding normalized eigenfunctions for various values of n and ℓquantum numbers. Numerical results, Schrödinger solutions, and special cases such as the modified screened Coulomb plus inversely quadratic Yukawa potential, Kratzer potential, Yukawa potential, and Coulomb potential were also considered. These results are largely consistent with previous studies.
Physica Scripta•Sep 19, 2023•3 citations