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