Lévy path integral approach to the fractional Schrödinger equation with δ-perturbed infinite square well

Abstract

Using a path integral approach, we consider a fractional Schrödinger equation with δ-perturbed infinite square well. The Lévy path integral, which is generalized from the Feynman path intergal for the propagator, is expanded into a perturbation series. From this, the energy-dependent Green’s function is obtained.