  Models of the spontaneous emission of photons coupled to the electronic
states of quantum dots are important for understanding quantum interactions in
dielectric media as applied to proposed solid-state quantum computers, single
photon emitters, and single photon detectors. The characteristic lifetime of
photon emission is traditionally modeled in the Weisskopf-Wigner approximation.
Here we model the fully quantized spontaneous emission, including near field
effects, of a photon from the excited state of a quantum dot beyond
theWeisskopf-Wigner approximation. We propose the use of discretized
central-difference approximations to describe single photon states via single
photon operators in 3+1 dimensions. We further show herein that one can shift
from the traditional description of electrodynamics and quantum
electrodynamics, in terms of electric and magnetic fields to one in terms of a
photonic wave function and its operators using the Dirac equation for the
propagation of single photons.
