Comments on "On the Consistency of the Solutions of the Space Fractional Schr\"odinger Equation" [J. Math. Phys. 53, 042105 (2012)]

TL;DR

This paper clarifies the proper treatment of integrals in the space fractional Schrödinger equation, confirming the consistency of previously proposed solutions through detailed analysis and analytic continuation techniques.

Contribution

It provides a detailed clarification of integral treatments and analytic continuation, reinforcing the validity of earlier solutions to the space fractional Schrödinger equation.

Findings

Proper integral treatment confirms solution consistency

Analytic continuation is essential for solution validity

Clarifies previous ambiguities in fractional quantum mechanics

Abstract

Recently we have reanalyzed the consistency of the solutions of the space fractional Schr\"odinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished. [doi: 10.1063/1.4705268]