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We investigate and compare different representations of the Riesz derivative,which plays an important role in anomalous diffusion and space fractionalquantum mechanics. In particular, we show that a certain representation of theRiesz derivative that is generally given as also valid for order alpha equals1, behaves no differently than the other definition given in terms of itsFourier transform. In the light of this, we discuss the alpha goes to 1 limitof the space fractional quantum mechanics and its consistency.

Definition of the Riesz Derivative and its Application to Space Fractional Quantum Mechanics