Scattering problems in the fractional quantum mechanics governed by the 2D space fractional Schrodinger equation

TL;DR

This paper investigates scattering problems in fractional quantum mechanics using the 2D space-fractional Schrödinger equation, deriving Green's functions and asymptotic formulas to approximate wave functions.

Contribution

It introduces mathematical expressions for Green's functions in 2D fractional Schrödinger equations and applies them to approximate scattering wave functions.

Findings

Derived Green's functions for 2D fractional Schrödinger equations

Provided asymptotic formulas for Green's functions

Obtained approximate wave functions for scattering problems

Abstract

The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions for the two cases. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems.