Exact path-integration for the two-dimensional Coulomb problem

Namik Kemal Pak, İ. Sökmen

K.V. Bhagwat, S. V. Lawande

Benjamín Raziel Jaramillo Avila, R. P. Martı́nez-y-Romero, H. N. Núñez‐Yépez +1 more

Namik Kemal Pak, İ. Sökmen

We describe a general method of applying point canonical transformations to the path integral followed by the corresponding new-time transformations aimed at reducing an arbitrary one-dimensional problem into an exactly solvable form. Our result is independent of operator-ordering ambiguities by construction. The method is used in getting the exact path-integral solutions of the Coulomb- and Morse-potential problems.

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.

SEJII SAKODA

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. 1