Consistency problem of the solutions of the space fractional Schrodinger equation

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Bayin S. S.

JOURNAL OF MATHEMATICAL PHYSICS, vol.54, no.9, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 9
  • Publication Date: 2013
  • Doi Number: 10.1063/1.4819502
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: No

Abstract

Recently, consistency of the infinite square well solution of the space fractional Schrodinger equation has been the subject of some controversy. Hawkins and Schwarz [J. Math. Phys. 54, 014101 (2013)] objected to the way certain integrals are evaluated to show the consistency of the infinite square well solutions of the space fractional Schrodinger equation [S. S. Bayin, J. Math. Phys. 53, 042105 (2012); 53, 084101 (2012)]. Here, we show for general n that as far as the integral representation of the solution in the momentum space is concerned, there is no inconsistency. To pinpoint the source of a possible inconsistency, we also scrutinize the different representations of the Riesz derivative that plays a central role in this controversy and show that they all have the same Fourier transform, when evaluated with consistent assumptions. (C) 2013 AIP Publishing LLC.