2011/04/04 by Fernando Nobre, Fernando D. Nobre, M. A. Rego-Monteiro +2 · 3 citations
Mathematics · Physics and Astronomy · #Dirac (video compression format) #Dirac equation #Exponential function #Fractional Differential Equations Solutions #Function (biology) #Klein–Gordon equation #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum #Quantum dynamics #Quantum mechanics #Relativistic quantum mechanics #Soliton #Statistical Mechanics and Entropy #Type (biology) #cond-mat.other #quant-ph
paper · pdf · doi:10.1103/physrevlett.106.140601
published as Physical Review Letters 106, 140601 (2011)
openalex publication_date 2011/04/04 · arxiv created 2011/04/28 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.