Consistency problem of the solutions of the space fractional Schrodinger equation


Creative Commons License

Bayin S. S.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.54, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 54 Konu: 9
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1063/1.4819502
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS

Özet

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.