1206.2513 (J. Weberszpil et al.)

Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic
Fractional Schrödinger Equation    [PDF]

J. Weberszpil, C. F. L. Godinho, A. Cherman, J. A. Helayël-Neto

The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\"odinger 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.

View original: http://arxiv.org/abs/1206.2513