Consistency Problem of the Solutions of the Space Fractional Schrödinger Equation
arXiv:1510.01687 · doi:10.1063/1.4819502
Abstract
Recently, consistency of the infinite square well solution of the space fractional Schrödinger equation has been the subject of some controversy. In [J. Math. Phys. 54, 014101 (2013)], Hawkins and Schwarz objected to the way certain integrals are evaluated to show the consistency of the infinite square well solutions of the space fractional Schrödinger equation [J. Math. Phys. 53, 042105 (2012); J. Math. Phys. 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. PACS numbers: 03.65.Ca, 02.50.Ey, 02.30.Gp, 03.65.Db
Misprints in Eqs.(68-70)corrected
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