On the quantum description of light in homogeneous conducting linear media

Abstract

In this paper, we use the Coulomb gauge, linear invariants and the dynamical invariant method in the framework of the Schrödinger equation to obtain a quantum description of light propagation through homogeneous conducting linear media with no charge density. We obtain exact wavefunctions for this problem in terms of solutions of a second-order ordinary differential equation which describes the amplitude of the classical damped harmonic oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations for each mode of the quantized electromagnetic field.