A general relation between the energy-dependent Green’s functions for different potentials is derived in a simple and direct manner. This interesting connection enables the eigenstates of one physical system to be deduced from those of a related system. The derivation is based on the Schrödinger equation and provides an independent justification for the technique of path-dependent time transformation used in path integration.

The Schrodinger-Green function is constructed for an anisotropic non-quadratic potential which has been studied in recent literature. The eigen energies and wavefunctions are readily obtained. Our analysis shows that the wavefunctions given in earlier literature are incorrect and the source of the error is pointed out. A semiclassical treatment of the problem is also presented in support of some of our observations.