  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.
