The Green function for the step potential via an exact summation of the perturbation series

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.…”

Green Function of Quantum Liouville Problem via Exact Summation of Perturbation Series

“…In the last decades, perturbation expansion of the path integral has been used to give the exact Green's functions for delta-function potential problems [2], [3], non-relativistic Coulomb system [4], inverse square potential [5], and to yield the Dirichlet boundary conditions for the nonrelativistic problems [6] and for the relativistic problems by summing the delta-function perturbation series [7]. Also the perturbative approach was recently successfully used for deriving the energy Green function for the step potential [8].…”

The propagator for step potential and mass using path decomposition method

“…Problems with a step potential and a rectangular barrier potential in [11,12] and [13] were exactly resolved with the spectral summation method [15]. In [3,10,13,16,17] and [18], the calculation by the path integral approach of the Green's function with piecewise flat potentials constituted a good generalizing step. A new interesting device in path integrals is the path decomposition method PDX which was invented by Aurbach and Kivelson [19].…”