Space-time transformations in radial path integrals

Ahmed Diaf, Mohammed Hachama

In this paper, we present analytic solutions of the Feynman propagator with the Rosen–Morse potential. To this end, an approximation of the centrifugal potential for any l state is used and nonlinear space–time transformations in the radial path integral are applied. A transformation formula that relates the original path integral to the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrödinger formalism. The Eckart potential is also treated as a special case.

Christian Grosche

In this Letter I present an alternative solution of the path integral for the radial Coulomb problem which is based on a two-dimensional singular version of the Levi–Civita transformation.

Takashi Ichinose

For the radial Dirac equation, a countably additive path space measure on the space of continuous paths living on the real half-line is constructed to give a path integral representation of its Green function.