Path Integrals in Polar and Spherical Coordinates

Pankaj Sharan

M. Victoria Carpio-Bernido

An explicit evaluation of the path integral in spherical polar coordinates for the Green function of a particle moving in an axially symmetric potential field is presented. A closed form of the Green function is obtained from which the energy eigenvalues and the normalized eigenfunctions are obtained as the poles and the residues at the poles, respectively.

A. M. Arthurs

Abstract The problem of summation over Feynman histories in curvilinear coordinates is discussed. Ordinary rules of calculus are used in conjunction with a Hamiltonian approach to the summation over histories. The procedure is illustrated by considering the propagator for dynamical systems in spherical polar coordinates.