Path-integral solutions for shape-invariant potentials using point canonical transformations

Abstract

Using a supersymmetric path-integral formulation, we give explicit point canonical transformations which map the kernels (or energy-dependent Green's function) of exactly known solvable shape-invariant potentials into those of two potential classes. Exact analytic expressions for the eigenvalues and eigenfunctions of these two classes of potentials are then retrieved following a standard procedure.