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Definition of the Riesz derivative and its application to space fractional quantum mechanics
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Date
2016-12-01
Author
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.
URI
https://hdl.handle.net/11511/63639
Journal
JOURNAL OF MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1063/1.4968819
Collections
Graduate School of Applied Mathematics, Article
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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.