A Schr\"odinger Equation for Light

TL;DR

This paper develops a Schr"odinger equation framework for single photons in a one-dimensional setting, revealing new features of the quantised electromagnetic field relevant to quantum relativity and photon localization.

Contribution

It introduces a Schr"odinger equation for localised photons, integrating relativistic and quantum aspects to uncover previously overlooked features of photon dynamics.

Findings

New features of the quantised EM field identified

Implications for quantum relativity discussed

Photon localization properties analyzed

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.