1998/08/10 by Samuel De Toro Arias, Christian Vanneste
Physics and Astronomy · #cond-mat.dis-nn
published as J. Phys. I France 7 (1997) 1071--1096 · 25 Revtex pages, 15 combined TeX Figures
arxiv created 1998/08/10 · arxiv updated 2009/11/30
The paper describes a formulation of discrete scalar wave propagation in an inhomogeneous medium by the use of elementary processes obeying a discrete Huygens' principle and satisfying fundamental symmetries such as time-reversal, reciprocity and isotropy. Its novelty is the systematic derivation of a unified equation which, properly tuned by a single parameter, leads to either the Klein-Gordon equation or the Schrödinger equation. The generality of this method enables one to consider its extension to other types of discrete wave equations on any kind of discrete lattice.