Abstract
Using a path integral approach, we consider a fractional Schrödinger equation with delta-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.
Highlights
Fractional quantum mechanics was first introduced by Laskin
It is described by the space-fractional Schrodinger equation (SFSE) containing the Riesz fractional operator
We consider an infinite square well with delta-function perturbation. This is an Open Access article published by World Scientific Publishing Company
Summary
Fractional quantum mechanics was first introduced by Laskin. It is described by the space-fractional Schrodinger equation (SFSE) containing the Riesz fractional operator. Following Feynman’s path integral approach to quantum mechanics, Laskin generalized the path integral over Brownian motions to Levy flights and obtained the space-fractional Schrodinger equation.[1, 2]. Solutions to the space-fractional Schrodinger equation with linear potential, delta potential, infinite square well, and Coulumb potential, have already been obtained via piece-wise solution approach, momentum representation method, and, indirectly, the Levy path integral approach.[3,4,5] despite the numerous works on fractional quantum mechanics, perturbation has not yet been explored. We consider the space-fractional Schrodinger equation with perturbative terms using the Levy path integral approach. We consider an infinite square well with delta-function perturbation This is an Open Access article published by World Scientific Publishing Company. Further distribution of this work is permitted, provided the original work is properly cited
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
