Definition of the Riesz derivative and its application to space fractional quantum mechanics

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2016-12-01

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Bayin, Selcuk S.

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We investigate and compare different representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics. In particular, we show that a certain representation of the Riesz derivative, Rax, that is generally given as also valid for alpha = 1, behaves no differently than the other definition given in terms of its Fourier transform. In the light of this, we discuss the alpha -> 1 limit of the space fractional quantum mechanics and its consistency. Published by AIP Publishing.

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https://hdl.handle.net/11511/63639

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.4968819

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Graduate School of Applied Mathematics, Article

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Citation Formats

S. S. Bayin, “Definition of the Riesz derivative and its application to space fractional quantum mechanics,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63639.