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

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2012-04-01

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Bayin, Selcuk S.

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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]

Subject Keywords

Path integral formulation, Generalized functions, Integral transforms , Anomalous diffusion , Fractional calculus, Integral equations, Wick rotation , Complex functions, Infinite square well , Schrodinger equations

URI

https://hdl.handle.net/11511/63875

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.4705268

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Graduate School of Applied Mathematics, Article

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Citation Formats

S. S. Bayin, “On the consistency of the solutions of the space fractional Schrodinger equation,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63875.