On the Problem of Electromagnetic-Field Quantization

TL;DR

This paper develops explicit solutions for the quantization of electromagnetic fields in cavities with varying dielectric media, addressing complex Hamiltonians and extending to randomly changing media.

Contribution

It provides explicit solutions to Heisenberg's equations for general quadratic Hamiltonians, advancing the understanding of electromagnetic-field quantization in complex media.

Findings

Explicit solutions for Heisenberg's equations of motion.

Application to quantization in media with random variations.

Framework for analyzing electromagnetic fields in complex cavities.

Abstract

We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations are obtained and applications to the radiation field quantization, including randomly varying media, are briefly discussed.