Nonlinear Relativistic and Quantum Equations with a Common Type of Solution

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