Exactness in the Path Integral of the Coulomb Potential in One Space Dimension
Abstract
Description
We solve time-sliced path integrals of one-dimensional Coulomb system in an exact manner. In formulating path integrals, we make use of the Duru-Kleinert transformation with Fujikawa's gauge theoretical technique. Feynman kernels in the momentum representation both for bound states and scattering states will be obtained with clear pole structure that explains the exactness of the path integral. The path integrals presented here can be, therefore, evaluated exactly by making use of Cauchy's integral theorem.
15 pages, no figure, to appear in Mod. Phys. Lett. A, added references and typos
15 pages, no figure, to appear in Mod. Phys. Lett. A, added references and typos