Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ Brazil.
Phys Rev Lett. 2011 Apr 8;106(14):140601. doi: 10.1103/PhysRevLett.106.140601. Epub 2011 Apr 4.
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→1. Interestingly, these equations present a common, solitonlike, traveling 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.
提出了量子物理的三个主要方程，即薛定谔方程、克莱因-戈登方程和狄拉克方程的推广。在这种情况下，考虑了具有依赖于指数 q 的指数的非线性项，使得在 q→1 时恢复标准线性方程。有趣的是，这些方程呈现出一种共同的、类孤子的、行波解，它是用 q-指数函数来表示的，这种函数在非广延统计力学中自然出现。在所有情况下，对于任意的 q 值，都保持了著名的爱因斯坦能量-动量关系。
