Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

Details Nonlinear Relativistic and Quantum Equations with a Common Type of Solution Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

2011-04-28

arxiv.org/abs/1104.5461v1

Physical Review Letters 106, 140601 (2011)

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, 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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