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arXiv · 1104.5461

Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

Fernando D. Nobre·Marco Aurelio Rego-Monteiro·Constantino Tsallis
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Abstract

Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way that the standard linear equations are recovered in the limit $q \rightarrow 1$. Interestingly, these equations present a common, soliton-like, travelling solution, which is written in terms of the $q$-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of $q$.

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Fernando D. Nobre, Marco Aurelio Rego-Monteiro, Constantino Tsallis. 2011-04-28. Nonlinear Relativistic and Quantum Equations with a Common Type of Solution. https://doi.org/10.1103/physrevlett.106.140601

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