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

Abstract

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.

References in corpus (4)

• Fractional Quantum Mechanics
• On the Consistency of the Solutions of the Space Fractional Schrödinger Equation
• Comments on "On the Consistency of the Solutions of the Space Fractional Schrödinger Equation" [J. Math. Phys. 53, 042105 (2012)]
• Levy flights in a box

Cited by in corpus (5)

• Fractional Schrödinger equation and time dependent potentials
• Self-accelerating beam dynamics in the space fractional Schrödinger equation
• Factorization of the Riesz-Feller fractional quantum harmonic oscillators
• Dissipative systems fractionally coupled to a bath
• Inflation and Primordial Perturbations in Fractal Cosmology