Green's function for the relativistic Coulomb system via sum over perturbation series

Abstract

We evaluate the Green's function of the D-dimensional relativistic Coulomb system via sum over perturbation series which is obtained by expanding the exponential containing the potential term V (x) in the path integral into a power series. The energy spectra and wave functions are extracted from the resulting amplitude.

Physical Vapor Deposition of Hexagonal and Tetragonal CuIn5Se8 Thin Films

“…To obtain the explicit result of g (n) k+β 0 , we note that [9] ∞ 0 dS The expression for g (n) k+β 0 (r b , r a ; E) can be obtained by induction with respect to n, and is given by…”

Path Integral Solution of the Aharonov–Bohm–Dyon System via Summing the Perturbation Expansions

“…A further reduction is given by takingg = 0. In this case, the Green's function of the relativistic A-B-C system reduces to that of the pure relativistic Coulomb system [6,14]. (ii) The Green's function of the relativistic A-B-D system reduces to that of the relativistic A-B-M system if α = 0.…”

Feynman Perturbation Series for the Morse Potential

“…Furthermore, among problems that can be exactly solved, there are few whose solutions can be obtained exactly by summing up the perturbation series in the path integral formalism [1]. Exact Green's functions: for delta-function [2]- [4], for Coulomb potential [5]- [7], for the inverse square potential [8] and for the step potential [9] are obtained by summing up the pertur-bation series in the path integral framework. In [2], the Feynman perturbation series are used to study the one-dimensional delta-function potential, where the authors extracted only correct informations for wave functions but they did not give the exact expression form of the propagator.…”

“…In [5], the perturbation series are used to derive the Green's function for the Coulomb potential in a closed analytical form. The Green's function of the one-dimensional relativistic Wood-Saxon, step and square well potential are evaluate by the Kleinert's path integral technique [6] and in [7] the same author has calculated the Green's function of the D-dimensional Coulomb by summing exactly the perturbation series; the energy spectra and wave functions are extracted. The exact propagator is derived by summing the Feynman perturbation series for a particle moving in the inverse square potential [8].…”