  We introduce a quantization scheme that can be applied to surface waves
propagating along a plane interface. An important result is the derivation of
the energy of the surface wave for dispersive non-lossy media without invoking
any specific model for the dielectric constant. Working in Coulomb's gauge, we
use a modal representation of the fields. Each mode can be associated with a
quantum harmonic oscillator. We have applied the formalism to derive
quantum-mechanically the spontaneous emission rate of surface plasmon by a
two-level system. The result is in very good agreement with Green's tensor
approach in the non-lossy case. Green's approach allows also to account for
losses, so that the limitations of a quantum approach of surface plasmons are
clearly defined. Finally, the issue of stimulated versus spontaneous emission
has been addressed. Because of the increasing density of states near the
asymptote of the dispersion relation, it is quantitatively shown that the
stimulated emission probability is too small to obtain gain in this frequency
region.
