A Schr\"odinger Equation for Light
Abstract
In this chapter we examine the quantised electromagnetic (EM) field in the context of a Schr\"odinger equation for single photons. For clarity we consider only a one-dimensional system. As a universal tool for calculating the time-evolution of quantum states, a Schr\"odinger equation must exist that describes the propagation of single photons. Being inherently relativistic, however, critical aspects of both special relativity and quantum mechanics must be combined when quantising the EM field. By taking the approach of a Schr\"odinger equation for localised photons, we will show how novel and previously overlooked features of the quantised EM field become a necessary part of a complete description of photon dynamics. In this chapter, I shall provide a thorough examination of new features and discuss their significance in topics such as quantum relativity and photon localisation.
Cite
@article{arxiv.2310.07366,
title = {A Schr\"odinger Equation for Light},
author = {Daniel Hodgson},
journal= {arXiv preprint arXiv:2310.07366},
year = {2023}
}
Comments
24 pages, 2 figures. This article will be published as a book chapter in Tahir, M B. ed. Schr\"odinger Equation - Fundamentals Aspects and Potential Applications: IntechOpen