Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

摘要

Generalizations of the three main equations of quantum physics, namely, theSchr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinearterms, characterized by exponents depending on an index $q$, are considered insuch 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 functionthat naturally emerges within nonextensive statistical mechanics. In all cases,the well-known Einstein energy-momentum relation is preserved for arbitraryvalues of $q$.