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On the consistency of the solutions of the space fractional Schrodinger equation

Bayin, Selcuk S.
Recently, it was pointed out that the solutions found in the literature for the space fractional Schrodinger equation in a piecewise manner are wrong, except the case with the delta potential. We re-analyze this problem and show that an exact and a proper treatment of the relevant integral prove otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schrodinger equation in general coordinates in terms of Fox's H-functions. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705268]