Wave Equation: An Overview

This book presents a quantum gravity theory based on unification of all quantum fields into a single field. The authors assess whether the equations of motion or the conservation equations are more fundamental. The application of this resolution to the Transmission Line Matrix modeling method for numerically solving the wave equation is also addressed. Flux density is proportional to the density of momentum. As such, the general procedure is described wherein this concept is applied to other Hermitian operators. An alternative metric is presented in this compilation which satisfies Einstein's field equations. This metric does not depend on weak field approximation, however it replaces Schwarzschild metric under certain conditions and provides an elegant solution for the rotation curves of galaxies as well as the energy levels of hydrogen atom. An optical wave equation for scattered light in materials with macroscopic spatial inhomegeneites is presented and analysed. The equation is applicable to variety of linear and nonlinear optical interactions in media with intrinsic, induced or engineered inhomegeneites. Lastly, the authors explore a black hole solution to the Jackiw-Teitelboim field equations for two-dimensional gravity. It turns out that the wave frequency is also connected to a suitable black hole metric, dilaton field, and cosmological constant.