Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic Fractional Schrödinger Equation
The main goal of this paper is to set up the coarse-grained formulation of a fractional Schrödinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding continuity equation is worked out and we also identify the contribution of the relativistic correction the quantum potential in the coarse-grained treatment. As a consequence, in the classical regime, we derive the sort of fractional Newtonian law with the quantum potential included and the fractional conterparts of the De Broglies's energy and momentum relations.
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