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arXiv · 1206.2513

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

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

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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BibTeXRIS

J. Weberszpil, C. F. L. Godinho, A. Cherman, J. A. Helayël-Neto. 2012-06-15. Aspects of the Coarse-Grained-Based Approach to a Low-Relativistic Fractional Schrödinger Equation. https://arxiv.org/abs/1206.2513

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