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Consistency problem of the solutions of the space fractional Schrodinger equation
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Date
2013-09-01
Author
Bayin, Selcuk S.
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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.
Subject Keywords
Mathematical Physics
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/63915
Journal
JOURNAL OF MATHEMATICAL PHYSICS
DOI
https://doi.org/10.1063/1.4819502
Collections
Graduate School of Applied Mathematics, Article
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S. S. Bayin, “Consistency problem of the solutions of the space fractional Schrodinger equation,”
JOURNAL OF MATHEMATICAL PHYSICS
, pp. 0–0, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63915.