Comment on: "On the consistency of solutions of the space fractional Schr\"odinger equation"

TL;DR

This paper critiques a previous proof claiming the consistency of certain solutions to the fractional Schrödinger equation, demonstrating that the earlier solutions are incorrect through proper calculation methods.

Contribution

It provides a corrected calculation showing that the previously proposed solutions do not satisfy the fractional Schrödinger equation for an infinite square well.

Findings

Previous solutions are invalid for the fractional Schrödinger equation.

Standard contour integral techniques are inappropriate for non-analytic integrands.

Corrected calculations support earlier findings of inconsistency.

Abstract

In [J. Math. Phys. 53, 042105 (2012)], Bay{\i}n claims to prove the consistency of the purported piece-wise solutions to the fractional Schr\"odinger equation for an infinite square well. However, his calculation uses standard contour integral techniques despite the absence of an analytic integrand. The correct calculation is presented and supports our earlier work proving that the purported piece-wise solutions do not solve the fractional Schr\"odinger equation for an infinite square well [M. Jeng, S.-L.-Y. Xu, E. Hawkins, and J. M. Schwarz, J. Math. Phys. 51, 062102 (2010)].