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

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Bayin S. S.

JOURNAL OF MATHEMATICAL PHYSICS, vol.57, no.12, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 12
  • Publication Date: 2016
  • Doi Number: 10.1063/1.4968819
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: Yes


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.