  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.
