On the Consistency of the Solutions of the Space Fractional Schrödinger Equation

Details On the Consistency of the Solutions of the Space Fractional Schrödinger Equation On the Consistency of the Solutions of the Space Fractional Schrödinger Equation

2012-03-19

arxiv.org/abs/1203.4556v1

JMP vol.53, no4, 042105 (2012)

Physics

Mathematical Physics

Scientific paper

10.1063/1.4705268

Recently it was pointed out that the solutions found in literature for the space fractional Schr\"odinger equation in a piecewise manner are wrong, except the case with the delta potential. We reanalyze this problem and show that an exact and a proper treatment of the relevant integral proves otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schr\"odinger equation in general coordinates in terms of Fox's H-functions.

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