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Journal of Physics A Mathematical and General

Relativistic fixed-energy amplitudes of the step and square well potential problems

De‐Hone Lin

Published Jun 21, 1997• 8 citations
Publisher

Abstract

The fixed-energy amplitudes (Green's function) of the one-dimensional relativistic Wood - Saxon, step and square well potential problems are calculated with the help of Kleinert's path integral technique for relativistic potential problems.
DOI
10.1088/0305-4470/30/12/022

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The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of \ensuremath{\delta}-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the strength of the \ensuremath{\delta}-function perturbation infinite repulsive produces a totally reflecting boundary, hence giving a path integral solution in half spaces in terms of the corresponding Green function. The example of the Wood-Saxon potential serves by an appropriate limiting procedure to obtain the Green function for the step potential and the finite potential well in the half space, respectively.
The formulation of the relativistic spinless path integral on the general affine space is presented. For the one dimensional space, the Duru-Kleinert (DK) method and the δδδ-function perturbation technique are applied to solve the relativistic path integrals of the smooth potential and the Dirichlet boundary condition problems, respectively.