Path integration for a class of noncentral potentials

Abstract

The path integral for the class of noncentral potentials, V(r,θ,ϕ) = f(r) + βr^-2csc²θ csc²ϕ + γr^-2csc²θ + δ r^-2sec²θ, is evaluated directly in polar coordinates. We obtain the propagator when f(r) is the harmonic oscillator potential, and the Green function when f(r) is an attractive Coulomb potential.